PreprintPDF Available
Preprints and early-stage research may not have been peer reviewed yet.

Abstract and Figures

Abstract: The galactic dynamics, the CMB anisotropies and the gravitational lensing do not agree with the observations. Either an additional component of mysterious unseen nonbaryonic matter (Dark Matter) is needed -to bridge the gap between theory and observations- or, the theory of gravity should be modified. We prove the spacetime is hyperbolic. The problems with dark matter — or rather, the cases where cold, collisionless dark matter makes predictions that conflict with observations — almost exclusively occur on small cosmic scales: scales of large individual galaxies and smaller. It’s true: certain modifications to gravity can better match the observations on these scales. All the experiments performed to detect Dark Matter were failed. The large structure spacetime is no longer flat. Hence the laws valid at flat space (e.g. Virial theorem ) fail to be valid at non-Euclidean spacetime. Gravity introduces nothing locally. All the effects of gravity are felt over extended regions of spacetime. Gravity is geometry. The first natural step is to modify the underlie geometry itself. We modify the equation of motion in the updated hyperbolic geometry that fits the data and predicts the observed flat rotation curve without invoking Dark Matter. The lensing could be interpreted as a curved spacetime. The missing mass required to account for the observed lens is the same as the missing mass required to account for the observed flat rotation curve. We show that our hyperbolic equation of motion predicts the kinematics of the UDGs and traces their speed rotation curves. The hyperbolic spacetime curvature –not Dark Matter- accounts for such a missing mass. CMB physics –and consequently its presumed Dark Matter as an initial condition- is in trouble after the tension in the value of Hubble constant. Thus, the hyperbolic structure of the spacetime, not dark matter, accounts for the current anomalies in the observations
Content may be subject to copyright.
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 38-72 www.itspoa.com/journal/er
The Hyperbolic Universe Does Not Need
Dark Matter - II
Salah A. Mabkhout1*
1 Department of Mathematics, Faculty of Education, Thamar University, Dhamar, Yemen
Email Address
salah622002@yahoo.com (Salah A. Mabkhout)
*Correspondence: salah622002@yahoo.com
Received: 15April 2022;Accepted: 30April 2022;Published: 8May 2022
Abstract:
The galactic dynamics, the CMB anisotropies and the gravitational lensing do not
agree with the observations. Either an additional component of mysterious unseen
nonbaryonic matter (Dark Matter) is needed -to bridge the gap between theory and
observations- or, the theory of gravity should be modified. We prove the spacetime is
hyperbolic. The problems with dark matter or rather, the cases where cold,
collisionless dark matter makes predictions that conflict with observations almost
exclusively occur on small cosmic scales: scales of large individual galaxies and
smaller. It‘s true: certain modifications to gravity can better match the observations on
these scales. All the experiments performed to detect Dark Matter were failed. The
large structure spacetime is no longer flat. Hence the laws valid at flat space (e.g.
Virial theorem
2
M V R G
) fail to be valid at non-Euclidean spacetime. Gravity
introduces nothing locally. All the effects of gravity are felt over extended regions of
spacetime. Gravity is geometry. The first natural step is to modify the underlie
geometry itself. We modify the equation of motion in the updated hyperbolic
geometry
2
r
V e r a
mmm

that fits the data and predicts the observed flat
rotation curve without invoking Dark Matter. The lensing could be interpreted as a
curved spacetime. The missing mass required to account for the observed lens is the
same as the missing mass required to account for the observed flat rotation curve. We
show that our hyperbolic equation of motion predicts the kinematics of the UDGs and
traces their speed rotation curves. The hyperbolic spacetime curvature not Dark
Matter- accounts for such a missing mass. CMB physics and consequently its
presumed Dark Matter as an initial condition- is in trouble after the tension in the
value of Hubble constant. Thus, the hyperbolic structure of the spacetime, not dark
matter, accounts for the current anomalies in the observations.
Keywords: Dark Matter, Flat curve, Hyperbolic spacetime, MOND , UDGs
1. Introduction
Using the power of the Doppler Shift, scientists can learn much about the motions
of galaxies. They know that galaxies rotate because, when viewed edge-on, the light
from one side of the galaxy is blue shifted and the light from the other side is red
shifted. One side is moving toward the Earth, the other is moving away. They can also
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 39-72 www.itspoa.com/journal/er
determine the speed at which the galaxy is rotating from how far the light is shifted.
Knowing how fast the galaxy is rotating, they can then figure out the mass of the
galaxy mathematically. As scientists look closer at the speeds of galactic rotation,
they find something strange. The individual stars in a galaxy should act like the
planets in our solar system, the farther away from the center, the slower they should
move. But the Doppler Shift reveals that the stars in many galaxies do not slow down
at farther distances. And on top of that, the stars move at speeds that should rip the
galaxy apart; there is not enough measured mass to supply the gravity needed to hold
the galaxy together. These high rotational speeds suggest that the galaxy contains
more mass than was calculated. Scientists theorize that, if the galaxy was surrounded
by a halo of unseen matter, the galaxy could remain stable at such high rotational
speeds. Another method astronomers use to determine the mass of a galaxy (or cluster
of galaxies) is simply to look at how much light there is. By measuring the amount of
light reaching the earth, the scientists can estimate the number of stars in the galaxy.
Knowing the number of stars in the galaxy, the scientists can then mathematically
determine the mass of the galaxy. Astronomers use the Mass Luminosity equation to
determine the mass of a star =
4. M=the star`s mass. L = the star‘s Luminosity.
Fritz Zwicky used both methods described here to determine the mass of the Coma
cluster of galaxies over half a century ago. When he compared his data, he brought to
light the missing mass problem. The high rotational speeds that suggest a halo
reinforce Zwicky‘s findings. The data suggest that less than 10% of what we call the
universe is in a form that we can see. Now scientists are diligently searching for the
elusive dark matter, the other 90% of the universe. Throughout the 1970s, however,
Rubin and other astronomers found the same pattern again and again, in galaxy after
galaxy, until theorists had little choice but to reach a consensus: Galaxies are
embedded within a vastly much larger, stabilizing halo of matter we can‘t detect in
any range of the electromagnetic spectrum - that is, matter that‘s ―dark‖. Theorists
even identified the properties of what the hypothetical matter might be, and
experimenters began designing instruments that in principle would be able to detect
the particle or collection of particles. Some theorists and observers have been
pursuing that possibility since the early 1980s, though the community generally has
seen their work as somewhat contrarian. The longer that dark matter went undetected,
Rubin said, the more likely she thought the solution to the mystery would be a
modification to our understanding of gravity. Maybe the discovery of dark matter was
not possible. Maybe dark matter doesn‘t exist. Maybe what she detected in the 1960s
and 1970s was evidence that gravity doesn‘t work on large scales in the manner that
Newton taught us [1].The conventional gravity approach has focused upon Newtonian
theory in the study of galactic dynamics as the galactic field is weak and the motions
is non relativistic. It was this approach that led to the inconsistency between the
theoretical Newtonian-based predictions and observations. Thus the intrinsically
linear Newtonian-based approach used has been inadequate for the description of the
galactic dynamics and the Einstein’s general relativity must be brought into the
analysis within the framework of established gravitational theory. This is an essential
departure from conventional thinking [2].
2. Dark Matter
The name ―Dark Matter‖ is an indication of its nonbaryonic nature: it cannot be
observed by emission of photons, so observers need to find a way around this problem.
Flat Rotation curve: A general observation of galaxy rotation can be stated as:
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 40-72 www.itspoa.com/journal/er
galaxies with a central bulge in their disk have a rotation curve which is flat from near
the centre to the edge, i.e. stars are observed to revolve around the centre of these
galaxies at a constant speed over a large range of distances from the centre of the
galaxy. However, it was expected that these galaxies would have a rotation curve that
slopes down from the centre to the edge in the same way as other systems with most
of their mass in the centre, such as the Solar System of planets or the Jovian System
of moons following the prediction of Keplers Laws. Something else is needed to
account for the dynamics of galaxies besides a simple application of the laws of
gravity to the observed matter. It is also observed that galaxies with a uniform
distribution of luminous matter have a rotation curve sloping up from center to edge.
Most low surface brightness galaxies rotate with a rotation curve that slopes up from
the center, indicating little core bulge. The galaxy rotation problem is the discrepancy
between observed galaxy rotation curves and the ones predicted assuming a centrally-
dominated mass that follows the luminous material observed. If masses of galaxies are
derived solely from the luminosities and the mass-to-light ratios in the disk and core
portions of spiral galaxies are assumed to be close to that of stars, the masses derived
from the kinematics of the observed rotation do not match. This discrepancy can be
accounted for if there exist a large amount of dark matter that permeates the galaxy
and extends into the galaxy's halo. Many physicists are nowadays convinced that
some form of dark matter has to exist to explain for instance the discrepancy between
the flat rotation curves of stars within a galaxy and the rotation curves expected from
Kepler's third law. Assuming flat space and circular orbit, astronomers use the Virial
theorem to determine the masses of the galaxies =2
. M is the mass of the
galaxy, V is the speed of the galaxy, R is the distance of the galactic center and G is
the gravitational constant [3].
Figure 1. The rotation curve of a galaxy (also called a velocity curve) is the plot of the orbital
speed (in km/s) of the stars or gas in the galaxy on the y-axis against the distance from the center
of the galaxy on the x-axis [4].
3. CMB Anisotropies
According to the theory of the Big Bang, the universe started hot and dense and
then expanded and cooled. In the hot, dense conditions of the early universe, photons
were tightly glued to matter. When the universe was about 300,000 years old the
temperature dropped below 3,000K allowing atomic hydrogen to form and releasing
the photons. These photons, which travelled freely through the universe as it
expanded and cooled, make up the cosmic microwave background (CMB) we see
today, with an average temperature of 2.7K. In the early universe, ordinary matter was
ionized and interacted directly with radiation via Thomson scattering. Dark matter
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 41-72 www.itspoa.com/journal/er
does not interact directly with radiation, but it does affect the CMB by its gravitational
potential (mainly on large scales), and by its effect on the density and velocity of
ordinary matter. Ordinary and dark matter perturbations, therefore, evolve differently
with time and leave different imprints on the cosmic microwave background (CMB).
Anisotropies observed to contain a series of acoustic peaks at near-equal spacing but
different heights. The first peak mostly shows the density of baryonic matter, while
the third peak relates mostly to the density of dark matter, measuring the density of
matter and the density of atoms. Current evidence for the existence of Dark Matter
comes from CMB anisotropies.
Figure 2. The WMAP 5-year "temperature angular power spectrum" (Nolta et al. 2009)
incorporating other recent results from the ACBAR (Reichardt et al. 2008, purple), Boomerang
(Jones et al. 2006, green), and CBI (Readhead et al. 2004, red) experiments. The red curve is the
best-fit CDM model to the WMAP data [5].
In addition, Big Bang nucleosynthesis provides evidence that some of the Dark
Matter may be baryonic. The inventory of observed baryons in the local universe falls
short of the total anticipated abundance from Big Bang nucleosynthesis implying that
most of the baryons in the universe are unseen. Anisotropies in the CMB are related to
anisotropies in the baryonic density field by the Sachs-Wolfe effect. This means that
the baryon density field variation at the time of decoupling can be linked to CMB
anisotropies. If all matter were made of baryons, the amplitude of the density
fluctuations should have reached
2
10d
at the present epoch. However, at the
present epoch (e.g., galaxies and galaxy clusters) we observe structures with
1d
[6]. The discrepancy can only be explained by the presence of additional matter,
which created potential wells for the baryons to fall into after decoupling. These
potential wells would have had to be formed by a weakly interacting fluid that
decoupled well before baryons and began to cluster much earlier. Such a fluid would
only interact via the gravitational and possibly the weak nuclear force. As the baryons
accumulated in the potential wells, their pressure would have built up, leading to
oscillations in the baryon fluid, termed baryon acoustic oscillations.(BAO). These
Oscillations leave an imprint on the CMB power spectrum, which has been confirmed
observationally, and which constrains the mass density, leading to a further
confirmation of the existence of this missing mass. Baryonic Acoustic Oscillations
(BAO) involves measuring the spatial distribution of galaxies to determine the rate of
growth of cosmic structure within the overall expansion of the universe. The patterns
of galaxy clustering contain information about how cosmic structure is amplified from
initial small fluctuations. This clustering encodes a robust ‗standard ruler‘ or ‗average
separation‘ between galaxies which could be used to map out the expansion history of
the universe in a manner analogous to type Ia supernova ‗standard candles‘. The
nature of this standard ruler is a preference for pairs of galaxies to be separated by a
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 42-72 www.itspoa.com/journal/er
co-moving distance of 150 Mpc. This favoured separation is an echo of sound waves
which propagated 13.3 billion years ago through the plasma before the Cosmic
Microwave Background epoch of recombination, about 380,000 years after the Big
Bang. However, In late July, scientists announced that the modern universe also looks
unexpectedly thin. Galaxies and gas and other matter haven‘t clumped together quite
as much as they should have. In the new research, members of the Kilo-Degree
Survey, or KiDS, observed about 31 million galaxies from up to 10 billion light-years
away. They then used these observations to calculate average distributions of the
universe‘s hidden gas and dark matter. They found clumps that are almost 10%
thinner than the forecast from the established cosmological model, known as Lambda
cold dark matter, or ΛCDM. They now seek to accomplish two contradictory tasks.
To solve the original problem of the expanding universe, they need a phenomenon
that would give the universe an extra kick outward. But to resolve the new anomaly,
they have to weaken the gravitational influence that makes the universe clump. When
you put the two problems together ―it becomes a nightmare to find an explanation for
both.‖ For example, to jump-start expansion, some theorists have tried adding ―dark
radiation‖ to the early universe. But they have to balance this extra radiation with
additional matter, which would have thickened the universe. So to end up with the
universe that we see, they have to invent additional interactions between the various
dark ingredients to get the desired thinness [11]. Well, as time goes on, that first, big
peak translates into a scale at which you‘re more likely to see two galaxies a certain
distance apart. Today, that distance corresponds to about 500 million light years,
meaning that if you pick a galaxy in the Universe, you‘re more likely to find a second
galaxy at a distance of 500 million light years than you are to find a second galaxy at
either 400 or 600 million light years. One can infer the Hubble constant from the size
of the largest fluctuations seen in the CMB. The CMB predictions for H0 assume that
the contents of the universe are well described by atomic matter, cold dark matter, and
dark energy. If this description is incomplete, the predictions could be wrong. There is
a tension between the value of the Hubble constant, H0, inferred from the local
distance ladder (H0=73(Km/sec)/Mpc) and the angular scale of fluctuations in the
Cosmic Microwave Background CMB (H0=67(Km/sec)/Mpc). The distance ladder
being model-independent while the CMB being model-dependent. The discrepancy in
the value of Hubble constant measured by the two methods shocks the CMB model
and consequently its presumed Dark Matter`s initial condition in the early universe. A
mathematical discrepancy in the expansion rate of the Universe is now ―pretty
serious‖, and could point the way to a major discovery in physics, says a Nobel
laureate; Prof Riess [7]. Finally, the value of the Hubble constant may be determined
indirectly from CMB data through the use of the ΛCDM model itself. CMB highly
dependent on the assumed energy content of the universe. The local measurement of
Ho is based on the astrophysics of stars.CMB results are based on the physics of the
early universe which is too speculative. With regard to CMB modeling, currently
observed discrepancies between measurements. The more interesting possibility is
that there is physics beyond the current standard model; possibilities include decaying
dark matter, evolving dark energy, dark radiation, modified gravity or deviations from
flatness.[8]
4. Gravitational Lensing
One of the consequences of general relativity is that massive objects (such as cluster
of galaxies) lying between a more distance source (such as a quasar) and an observer
should act as a lens to bend the light from this source. Galaxy clusters exhibit the
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 43-72 www.itspoa.com/journal/er
phenomenon of gravitational lensing. Because the gravitational field of the cluster
curves the spacetime around it. The curvature of the galaxy’s spacetime acts as a
gigantic deforming lens. Strong lensing is the observed distortion of background
galaxies into arcs when their light passes through such a gravitational lens. By
measuring the distortion geometry, the mass of the intervening cluster can be obtained.
The mass-to-light ratios obtained correspond to the dynamical Dark Matter
measurements of clusters. Besides galactic dynamics, the amount of lensing of
galaxies around galaxy clusters is too high to be caused by the visible matter. Apart
from the stars themselves, a galaxy cluster also has a gas component, but X-ray
observations show that this is still not enough to account for the extra mass. The
cluster must therefore have a non-emitting halo of Dark Matter around it.The Dark
Matter warps the galaxys spacetime.
The Universe seems lumpier than it should be: The large mass of a galaxy cluster
deflects light from background objects, a phenomenon known as gravitational lensing.
The large-scale gravitational lens caused by the whole cluster can be modified by
smaller-scale mass concentrations within the cluster, such as individual galaxies.
Meneghetti et al. examined these small-scale gravitational lenses in observations of
11 galaxy clusters. They found an order of magnitude more small-scale lenses than
would be expected from cosmological simulations. The authors conclude that there is
an unidentified problem with either prevailing simulation methods or standard
cosmology. Cold dark matter (CDM) constitutes most of the matter in the Universe.
The interplay between dark and luminous matter in dense cosmic environments, such
as galaxy clusters, is studied theoretically using cosmological simulations.
Observations of gravitational lensing are used to characterize the properties of
substructuresthe small-scale distribution of dark matter - in clusters. We derive a
metric, the probability of strong lensing events produced by dark-matter substructure,
and compute it for 11 galaxy clusters. The observed cluster substructures are more
efficient lenses than predicted by CDM simulations, by more than an order of
magnitude. They suggest that systematic issues with simulations or incorrect
assumptions about the properties of dark matter could explain their results. Because
dark matter's effects are detectable via gravity, we can ―see‖ the presence of dark
matter via its gravitational-lensing effects. In a few cases, we've even detected lensing
where little matter is present. That's one of the many pieces of evidence in favor of
dark matter. Features of the Cosmic Microwave Background can be explained by the
presence of dark matter. And models of the early Universe produce galaxies and
galaxy clusters by building on structures formed by dark matter. The fact that these
models get the big picture so right has been a strong argument in their favor. But a
new study suggests that the same models get the details wrongby an entire order of
magnitude. The people behind the study suggest that either there's something wrong
with the models, or our understanding of dark matter may need an adjustment. The
new study, performed by an international team of researchers decided to use
gravitational lensing to determine whether the dark matter distribution seen in the
models matched where we see it via gravitational lensing. They've built models of the
early Universe that indicate how dark matter helped structure the first galaxies and
drew them into clusters of galaxies. These models, when run forward, provide a
description of what that dark matter distribution should look like at different points in
the Universe's history up to the present. The researchers found a strong agreement
between the appearance of lensed objects and the location of individual galaxies,
which allowed them to validate their mass-distribution calculations. The researchers
then used the Universe simulator to build 25 simulated clusters and performed a
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 44-72 www.itspoa.com/journal/er
similar analysis with the clusters. The two didn‘t match. There were significantly
more areas that generated high distortion in the real-Universe galaxy than there were
in the model. This would be the case if the distribution of dark matter were a bit more
lumpy than the models would predictthe dark matter halos around galaxies were
more compact than the models would predict. This isn‘t the first discrepancy of the
sort we‘ve seen. Dark matter models also predict that there should be more dwarf
satellite galaxies around the Milky Way and that they should be more diffuse than
they are. But if we were to adjust our models to make these galaxies more diffuse,
we'd be less likely to see more compact structures in galaxy clusters. So rather than
finding two problems that could both be solved by making one adjustment, the two
issues appear to need adjusting in opposite directions [9].
However, if the cluster‘s spacetime is not flat; the lensing could be interpreted as a
curved spacetime, not via the existence of Dark Matter. The missing mass required to
account for the observed lens is the same as the missing required to account for the
observed flat rotation curve. The hyperbolic spacetime curvature not Dark Matter-
accounts for such missing mass, as we shall prove later.
5. Study Rules Out Dark Matter Destruction as Origin of Extra
Radiation in Galaxy Center
Dark matter annihilation is smaller: Cosmological models in which dark matter
consists of cold elementary particles predict that the dark halo population should
extend to masses many orders of magnitude below those at which galaxies can form.
Here they report a cosmological simulation of the formation of present-day haloes
over the full range of observed halo masses (20 orders of magnitude) when dark
matter is assumed to be in the form of weakly interacting massive particles of mass
approximately 100 gigaelectron-volts. The simulation has a full dynamic range of 30
orders of magnitude in mass and resolves the internal structure of hundreds of Earth-
mass haloes in as much detail as it does for hundreds of rich galaxy clusters. They
find that halo density profiles are universal over the entire mass range and are well
described by simple two-parameter fitting formulae. Halo mass and concentration are
tightly related in a way that depends on cosmology and on the nature of the dark
matter. For a fixed mass, the concentration is independent of the local environment for
haloes less massive than those of typical galaxies. Haloes over the mass range of 10−3
to 1011 solar masses contribute about equally (per logarithmic interval) to the
luminosity produced by dark matter annihilation, which we find to be smaller than all
previous estimates by factors ranging up to one thousand[10]. The detection more
than a decade ago by the Fermi Gamma Ray Space Telescope of an excess of high-
energy radiation in the center of the Milky Way convinced some physicists that they
were seeing evidence of the annihilation of dark matter particles, but a team led by
researchers at the University of California, Irvine has ruled out that interpretation.
They were able to determine that the observed gamma rays could not have been
produced by what are called weakly interacting massive particles, most popularly
theorized as the stuff of dark matter. In this paper, they are eliminating dark matter
candidates over the favored range, which is a huge improvement in the constraints we
put on the possibilities that these are representative of dark matter.‖ Oscar Macias, a
postdoctoral scholar in physics and astronomy at the Kavli Institute for the Physics
and Mathematics of the Universe at the University of Tokyo whose visit to UCI in
2017 initiated this project: ―We took over three years to pull all of these new, better
models together and examine the emissions, finding that there is little room left for
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 45-72 www.itspoa.com/journal/er
dark matter.‖ [11]. Kaplinghat noted that physicists have predicted that radiation from
dark matter annihilation would be represented in a neat spherical or elliptical shape
emanating from the Galactic Center, but the gamma ray excess detected by the Fermi
space telescope after its June 2008 deployment shows up as a triaxial, bar-like
structure. ―If you peer at the Galactic Center, you see that the stars are distributed in a
boxy way,‖ he said. ―There‘s a disk of stars, and right in the center, there‘s a bulge
that‘s about 10 degrees on the sky, and it‘s actually a very specific shape sort of an
asymmetric box and this shape leaves very little room for additional dark matter.‖
[12].
6. MACHOs
The Massive Compact Halo Objects (MACHOs), objects like black holes, and
neutron stars that purportedly populate the outer reaches of galaxies like the Milky
Way. Then there are the Weakly Interacting Massive Particles (WIMPs), which
possess mass, yet do not interact with ordinary matter (baryons such as protons and
neutrons) because they are composed by something unknown. Dark (missing) matter
(DM) even comes in two flavors, hot (HDM) and cold (CDM). The CDM is
supposedly to be in dead stars, planets, brown dwarfs (failed stars) etc., while HDM
is postulated to be fast moving in particles floating throughout the universe. It should
be constituted by neutrinos, tachyons etc. But where is all of this missing matter? The
truth is that after many years of looking for it, there is still no definitive proof that
WIMPs exist, or that MACHOs will ever make up more than five percent of the total
reserve of missing dark stuff.
Machos and Black holes: Some scientists are revisiting an old idea that black holes
born at the dawn of time are a prime suspect for all that missing mass. Researchers
call these speculative black holes ―massive compact halo objects,‖ or MACHOs, since
dark matter lurks in a ―halo‖ in and around big galaxies. But a new study in The
Astrophysical Journal Letters offers a serious reality check to the idea that MACHOs
are dark matter. In late January, physicists at Johns Hopkins University in Baltimore,
Maryland, sat down to discuss the rumours that the Laser Interferometer
Gravitational-Wave Observatory (LIGO), a pair of ground-based, 4-kilometre-long
instruments, had spotted the merger of two black holes of around 30 solar masses.
These rumors were later confirmed as the first detection of gravitational waves, a
phenomenon predicted by Albert Einstein that had escaped detection for 100 years
But their lunchtime chat quickly turned to a different mystery dark matter. Because
the collapse of a single star normally cant make such heavy black holes, they
wondered if the merging objects might be leftovers from the Big Bang. If so, could
the very early Universe have produced lots of similarly sized primordial black holes?
And could these black holes be the dark matter that holds galaxies together? ―When
you don't know what something is, you have to consider everything,‖ says Simeon
Bird, one of the physicists at Johns Hopkins. The numbers looked good. The mass of
the black holes was within a range that earlier searches for dark matter had not ruled
out, and the time it took LIGO to spot the event was compatible with the merger rate
that scientists had predicted. In May, Bird and his colleagues turned their discussion
into a paper, and the theory sparked a frenzy of media coverage around the world. The
idea soon received a boost. In June, it was suggested that primordial black holes could
also explain the uneven distribution of infrared light in the cosmic background. By
August, a team led by astrophysicist Misao Sasaki of Kyoto University in Japan
largely corroborated Birds theory, but suggested that such black holes might account
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 46-72 www.itspoa.com/journal/er
for only a fraction of dark matter. Timothy Brandt, an astrophysicist at the Institute
for Advanced Study, wrote the study after he took a close look at 11 dim, feeble, and
weird little galaxies. Astrophysicist Timothy Brandt thinks that he has found a fatal
flaw with Birds theory. Brandt, looked at the motion of stars within ten well-studied
dwarf galaxies close to the Milky Way. The movements of the few stars that are
visible reveal the presence of around 100 times more matter than can be seen. But
when Brandt looked closer, he found that the stars are moving too slowly, and are
concentrated too tightly, for the invisible mass to be in the form of 30-solar-mass
black holes. Stars in a galaxy exchange energy as they pass each other; massive stars
or black holes transfer energy to smaller stars, speeding their orbits and spreading the
stars out. But in these galaxies, that wasn‘t happening. ―Either they arent sharing
energy, or there aren't these massive black holes hanging around,‖ Brandt says [13].
The stars there are choking with dark matter, at least compared to larger galaxies like
the Milky Way or Andromeda, but the little galaxies don‘t seem to show any obvious
signs of harboring a flotilla of old black holes. These galaxies would be less dense and
larger than we see. Instead they‘re inexplicably compact. And that could represent a
big threat to the MACHO hypothesis. Meanwhile, ultra-faint dwarf galaxies are
roughly 99% dark matter.―The dark matter is holding them together and preventing
them from flying apart‖, Brandt says. And that's where Brandt realized he could see if
a bunch of old black holes between 20 to 100 times the mass of the sun (a size range
for MACHOs that has yet to be ruled out) really exist there. If so, they‘d accelerate
stars as they passed nearby, causing the entire cluster or galaxy to ―puff‖ outward over
billions of years. A diffuse cloud of dark matter particles, on the other hand, would
keep the cluster glued together [14].
MACHOs and Brown dwarfs: Brown dwarfs are substellar objects that occupy the
mass range between the heaviest gas giant planets and the lightest stars, of
approximately 13 to 7580 Jupiter masses, or approximately 2.5×10² kg to about
1.5×10² kg. Brown dwarfs are failed stars about the size of Jupiter, with a much larger
mass but not quite large enough to become stars. Like the sun and Jupiter, they are
composed mainly of hydrogen gas, perhaps with swirling cloud belts. Unlike the sun,
they have no internal energy source and emit almost no visible light. Brown dwarfs
are formed along with stars by the contraction of gases and dust in the interstellar
medium. The star formation process does not seem to produce mass function which
can hide significant dark matter in brown dwarfs [15]. Brown dwarfs are so elusive,
so hard to find. Brown dwarfs won‘t account for all of the so-called dark matter.
There are brown dwarfs, and maybe small black holes, and faint white dwarfs regular
stars that lost their outer gaseous envelopes leaving the burned-out core of old stars.
White dwarfs, brown dwarfs, black holes and gas account for some of the dark matter.
The rest presumably is a new form of matter"[16].
MACHOs are dead: Decades of research have narrowed down the possibilities.
Early favourites included not only black holes, but also other massive compact halo
objects (MACHOs) made of ordinary matter. Brown dwarfs won‘t account for all of
the so-called dark matter. A series of studies, however, gradually ruled out most of the
possibilities. For example, researchers determined that black holes between about
one-thousand billionth and one-billionth the mass of the Sun would destroy neutron
stars. The presence of neutron stars in ancient globular clusters therefore suggests that
primordial black holes of this size are extremely rare and could not account for all the
dark matter in the Universe. Bird's theory was based on the fact that no one had yet
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 47-72 www.itspoa.com/journal/er
ruled out larger black holes. But in the view of theoretical physicist John Ellis of
King‘s College London, ―MACHOs are dead‖ he said [13].
7. WIMPs
A decade ago, physicists were largely convinced that dark matter was made up of
weakly interacting massive particles (WIMPs). These are subatomic particles that
have mass, but lack a charge (so they respond to gravity, but not to light or
electromagnetism). Most scientists think that dark matter is composed of non-
baryonic matter. The lead candidate, WIMPS (weakly interacting massive particles),
have ten to a hundred times the mass of a proton, but their weak interactions with
―normal‖ matter make them difficult to detect. Neutralinos, massive hypothetical
particles heavier and slower than neutrinos, are the foremost candidate, though they
have yet to be spotted. The smaller neutral axion and the uncharched photinos are also
potential placeholders for dark matter. WIMPs are predicted by a theory called
Supersymmetry. This is an extension of the standard model of particle physics devised
to fix some inconsistencies with observed physics. It posits that symmetry between
two fundamental classes of particle - bosons, such as photons and the Higgs boson,
and fermions, such as protons and electrons - produces superpartners in the other
class that differ in mass, but are otherwise .similar ―Supersymmetry is beautiful
mathematically,‖ says physicist Oliver Buchmueller of Imperial College London.
―With just one weakly interacting particle, we can explain all the dark matter we see
in the Universe.‖ Indeed, so well does the lightest of these hypothetical particles fit
the bill for dark matter that it has been called ―the WIMP miracle‖, says physicist
Leslie Rosenberg of the University of Washington in Seattle. But supersymmetrical
particles have proved maddeningly elusive. Physicists at CERN, Europes particle-
physics laboratory, are searching for WIMPs with the Large Hadron Collider (LHC)
by smashing protons or atomic nuclei together to recreate the conditions of the early
Universe. Elsewhere, researchers are looking for signs of the particles bumping into
sensitive detectors or affecting astronomical objects. No sign of supersymmetric
particles or dark matter at masses up to 1,600 GeV, where physicists had expected to
find them. Weakly interacting massive particles (WIMPs) are the leading candidates.
Other possibilities include a potentially very light particle called the axion and a more
recent proposal the very heavy Planckian interacting massive particle. The search
for the particles is ongoing. Physicists at CERN's Large Hadron Collider are looking
for WIMPs, the Axion Dark Matter Experiment is running at the University of
Washington, Seattle, and China has launched the Dark Matter Particle Explorer. To
understand dark matter, researchers need to uncover how it affects the Universe
around it. But so far the only known effect is gravitational pull. This paucity of
information makes it hard to know whether dark matter is a particle, a field or a
misunderstanding of how gravity works. Astronomical observations are continuing.
Meanwhile, in mines under Ontario in Canada, the PICO experiment is aiming high-
speed cameras at detectors filled with super-heated fluids to look for signs of dark
matter interacting with ordinary matter [17]. When it comes to detecting dark matter,
neutrinos will eventually get in the way. Arthur McDonald, director of the Sudbury
Neutrino Observatory in Ontario, who won the 2015 Nobel Prize in Physics for his
part in the discovery of neutrino oscillations, explains why: There are two schools of
thought on dark matter. One is that it is embodied in a theoretical particle called an
axion. CERN Axion Solar Telescope (CAST) experiment, which used a prototype
magnet for the Large Hadron Collider to look for axions that might have been
produced in the Sun's core. None have been seen. The second line of thinking is that
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 48-72 www.itspoa.com/journal/er
dark matter is weakly interacting massive particles (WIMPs), perhaps predicted by a
proposed extension of the standard model of particle physics called Supersymmetry.
Direct detection of WIMPs involves looking for their occasional collisions with
ordinary matter. No sign of supersymmetric particles or dark matter at masses up to
1,600 GeV, where physicists had expected to find them [17]. The latest results from
two direct detection experiments have ruled out theoretically attractive dark matter
candidates, including WIMPs: Scientists from two of the world‘s biggest dark matter
detectors have reported that their latest experiments, like all earlier attempts, have
produced no sign of the elusive substance. In a pair of papers published in Physical
Review Letters, researchers from the XENON1T and PandaX-II collaborations have
ruled out some theoretical possibilities for dark matter particles and narrowed down
the search area for future experiments. Two independent experimental
collaborationsXENON and PandaX-IIhave recently taken the next steps in this
relentless march of progress. The former group has built the world‘s largest dark
matter detector, called XENON1T. It utilizes a 2000-kg target of liquid xenon, housed
in a 10-m-tall water tank located 1.4 km underground in the low-background
environment of central Italy‘s Gran Sasso National Laboratory. PandaX-II, by
contrast, is located 2.4 km below ground in the China Jinping Underground
Laboratory in Sichuan, China, and consists of 584 kg of liquid xenon. The reason both
experiments use xenon is twofold. First, it is highly unreactive, helping to maintain
the required low rate of background events. Second, its nucleus is relatively high in
mass (containing 131 nucleons on average), providing a big target for incoming dark
matter particles. If one of these particles were to pass through the Earth and then
collide with a xenon nucleus in XENON1T [18] or PandaX-II [19] that interaction
could produce a faint but detectable signal of light (scintillation) and electric charge
(ionization). Observing even a handful of such events would put us well on the way to
identifying the nature of the mysterious substance that makes up our Universe‘s dark
matter. The recent publications from the XENON and PandaX-II collaborations do
not claim to have detected any particles of dark matter. For example, a class of
scenarios that has recently attracted a lot of attention is that in which the dark matter
is but one of several particle species that make up a ―hidden sector‖. Because hidden
sector particles do not directly couple to ordinary particles, they can be very difficult
to detect in underground experiments and hard to produce at accelerators. And at the
same time, experimental progress is being made as well. Proposals for new and
different kinds of experiments abound, with the goal of testing an ever wider range of
previously overlooked candidates for dark matter. Because of the progress of
experiments such as XENON1T and PandaX-II, the field of dark matter research is
currently in a state of major disruption. The dark matter, it turns out, is not what many
of us in the particle theory community imagined it was likely to be. The lack of a
definitive detection of dark matter particles, in both underground experiments and at
the Large Hadron Collider, has had a palpable effect on the community of scientists
that study particle dark matter. Time passes without a confirmed detection, even the
most heavily backed theories are beginning to look less likely. A series of
experiments have systematically searched for, and failed to find, the theoretical
candidates for dark matter - one by one, the possibilities are being reduced. The
longer the puzzle goes unsolved, the more twitchy the scientific community will
become. ―People are a little nervous,‖ says Rosenberg. The existence of dark matter
has been inferred from the motion of stars since the 1930s, but its nature remains a
mystery. The dark-matter particle posited by the most popular theory has not been
shown to exist - if it is to make an appearance, it may be now or never. The search is
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 49-72 www.itspoa.com/journal/er
narrowing and the possibilities are dwindling; physicists may soon have to move on to
alternative explanations [20].
A raft of experiments designed to finally detect, or refute, the remaining candidates
are now underway, each with vastly different approaches to the problem. As more
options are crossed off the list, physicists may have to explore new ideas and
reconsider alternative theories such as Birds - or accept that nature may have hidden
dark matter just out of our reach [13]. Does the existence of dark matter particles
constitute a scientific theory? Could the existence of dark matter particles be
falsifiable? ―When you don‘t know what something is, you have to consider
everything,‖ But even nondetections constitute progress, in that they reveal to us what
the dark matter is not!!! Does this make sense, to rule out what is not dark matter?
Potato is not dark matter and tomato also is not dark matter …etc indefinitely. The
process of ruling out dark matter candidates would continue indefinitely, by this sense
it seems not falsifiable. Like supersymmetric particles, every time we fail to detect
them, we move the constraints to untouchable level!!! Dark Matter hypotheses are
too flexible to be falsifiable. Different projects measure different values for Dark
Matter: Dark Energy Survey (DES) 26%, Planck 29% and WMAP`s 23%! [21].
8. Most Early Massive Galaxies Are Strongly Dominated by Normal
Matter
The theory is that galaxies contain dark matter and that this makes them
gravitationally stable in the standard model of physics. McCulloch is skeptical about
dark matter and he says that it is an implausible theory to explain dwarf galaxies,
which are super-tiny galaxies containing only between 1,000-10,000 stars that revolve
around the milky way. There are 20 dwarf galaxies in existence from Segue-1 (the
smallest) to Canes Venatici-1 (the largest), and dark matter is only meant to work by
spreading out across a wide distance, but it is still used to explain dwarf galaxies, even
though this requires dark matter to be concentrated within these systems, which is
implausible. In a study published in Nature, researchers have now looked at six
massive, star-forming galaxies from when the universe was around four billion years
old. These distant galaxies were observed using the ESOs Very Large Telescope,
which allowed researchers to measure the rotation of the galaxies. Their findings were
something of a surprise. Unlike the spiral galaxies we see today, the outer regions of
the six observed appear to be rotating far slower than the areas close to their centers
a finding that is at odds with simulations of how early galaxies form. It also suggests
that there is less dark matter present compared to galaxy we see today. Reinhard
Genzel, lead author of the study, explained: Surprisingly, the rotation velocities are
not constant, but decrease further out in the galaxies. There are probably two causes
for this. Firstly, most of these early massive galaxies are strongly dominated by
normal matter, with dark matter playing a much smaller role than in the Local
Universe. Secondly, these early discs were much more turbulent than the spiral
galaxies we see in our cosmic neighborhood.[22]
Apart from flat rotation curves, evidence for dark matter comes from the small
anisotropies in the cosmic microwave background radiation(CMB), which suggests
that forming large scale cosmic structures on time scales shorter than the Hubble time
essentially requires substantial amount of gravitating cold dark matter. Most early
massive galaxies are strongly dominated by normal matter ruled out the speculations
that the Theory of large scale structure formation requires anisotropies in the CMB,
but also requires the presence of dark matter in early universe. [24]
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 50-72 www.itspoa.com/journal/er
Figure 3. Most early massive galaxies are strongly dominated by normal matter [23].
9. Dwarf Galaxies Dont Fit Standard Model and Challenges Cold
Dark Matter Cosmology
Dwarf galaxies that orbit the Milky Way and Andromeda galaxies defy the accepted
model of galaxy formation, and recent attempts to wedge them into the model are
flawed, Yet Centaurus A is the third documented example, behind the Milky Way and
Andromeda, of a vast polar structure" in which satellite dwarves co-rotate around a
central galactic mass in ―preferentially oriented alignment.‖―The model predicts that
dwarf galaxies should form inside of small clumps of dark matter and that these
clumps should be distributed randomly about their parent galaxy,‖―But what is
observed is very different. The dwarf galaxies belonging to the Milky Way and
Andromeda are seen to be orbiting in huge, thin disk-like structures. ‖Centaurus A, an
elliptical galaxy 13 million light-years from Earth, hosts a group of dwarf satellite
galaxies co-rotating in a narrow disk, a distribution not predicted by dark-matter-
influenced cosmological models. ―So this means that we are missing
something, ‖Pawlowski said [25]. ―Either the simulations lack some important
ingredient, or the underlying model is wrong. This research may be seen as support
for looking into alternative models.‖[6]. Standard model fails to replicate what's
observed and therefore they seek alternatives. Dark matter is thought to be an as-yet
undetected matter that provides galaxies with enough mass to prevent the speed of
their rotation from pulling them apart. If present, the unseen cloud of matter would be
extremely unlikely to result in the planar structures seen. ―There‘s a very serious
conflict, and the repercussion is we do not seem to have the correct theory of gravity‖.
―When you have a clear contradiction like this, you ought to focus on it,‖said David
Merritt, professor of astrophysics at Rochester Institute of Technology and co-author
of the new study. ―This is how progress in science is made.‖ Even though a discovery
could very plausibly be right around the corner, there is a widespread view that many
of the most theoretically attractive candidates for dark matter should have been
detected by now, based on their predicted properties. In the absence of such a
discovery, the field has begun to redirect efforts toward new, and sometimes very
different, ideas. Combined with negative results from American LUX experiment and
tests at the Large Hadron Collider, these results are adding to a sense of frustration
among researchers.
10. Bullet Cluster
From the X-ray observations, the scientists inferred that the collision speed of the
galaxies in the Bullet Cluster must have taken place at approximately 3000 km/s. But
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 51-72 www.itspoa.com/journal/er
such high collision speeds almost never occurred in the computer simulations based
on particle dark matter. The scientists estimated the probability for a Bullet-Cluster-
like collision to be about one in ten billion, and concluded: that we see such a
collision is incompatible with the concordance model. And that‘s how the Bullet
Cluster became strong evidence in favor of modified gravity. However, a few years
later some inventive humanoids had optimized the dark-matter based computer
simulations and arrived at a more optimistic estimate of a probability of 4.6×10-4 for
seeing something like the Bullet-Cluster. Briefly later they revised the probability
again to 6.4×106. Either way, the Bullet Cluster remained a stunningly unlikely event
to happen in the theory of particle dark matter. It was, in contrast, easy to
accommodate in theories of modified gravity, in which collisions with high relative
velocity occur much more frequently. The Bullet Cluster isn‘t the incontrovertible
evidence for particle dark matter. It‘s possible to explain the Bullet Cluster with
models of modified gravity. And it‘s difficult to explain it with particle dark matter
[26]. The greatest challenge to modified gravity theories, and also the clearest direct
evidence of Dark Matter, comes from observations of a pair of colliding galaxy
clusters known as the Bullet Cluster in which the stars and Dark Matter separate from
the substantial mass of ionized gas. The Dark Matter follows the less substantial stars
and not the more massive gas. Since the new bullet cluster is less massive and the
merger slower, weighing its dark matter could be harder. The dark matter hypothesis
for the bullet cluster is contradicted by the cold dark matter ΛCDM model. The initial
relative velocity of the two colliding clusters would need to be around 3000 km/s in
order to explain the observed shock velocity, X-ray brightness ratio and morphology
of the main and sub-cluster. Jounghun and Eiichiro (2010) have shown that such a
high infall velocity is incompatible with the predictions of the cold dark matter
ΛCDM model. The probability that such an event could occur is roughly one in 10
billion![27].
Figure 4. Bullet Cluster. [28]
11. The DAMA Results Were Not Independently Replicable
While the astrophysical evidence supporting the existence of dark matter is
overwhelming, every experiment designed and built to directly detect whatever
particle might be responsible for dark matter has come up empty. Every experiment,
that is, except one: the DAMA/LIBRA experiment. While other experiments that are
far more sensitive - including Super CDMS, XENON, Edelweiss, LUX, and many
others - have only detected negative results down to extreme precisions,
DAMA/LIBRA has continuously observed a significant signal for about 20 years: As
Earth moves around the Sun and through the dark matter particles populating the
entire galaxy, we should see what‘s called an ―annual modulation.‖ During part of the
year, the Earth should be moving with the Sun in its orbit around the galaxy, and so
it‘s passing more quickly through the dark matter particles that are present in the
galaxy. Six months later, the Earth should be moving maximally against the Sun‘s
motion, decreasing the speed that the Earth moves through the galaxy‘s dark matter. If
even a fraction of the signal that‘s produced in such a detector is due to dark matter,
that portion of the signal will increase and decrease in a periodic fashion with a period
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 52-72 www.itspoa.com/journal/er
of precisely one year. What it began seeing, almost immediately, was a significant
annual modulation in the event rate of the detector. Without an understanding of their
noise background, however, much of the community has long been skeptical. Even as
20 years of data now yields an unambiguously significant result in a world where a
5-sigma result is the gold standard.
At last, the critical test has been performed: a completely independent team, ANAIS,
has carried out an identical experiment to DAMA/LIBRA, replicating the study and
testing its validity. With three complete years of data collected, ANAIS has ruled out
the DAMA/LIBRA results in a model-independent way to better than 99% confidence.
The world‘s most controversial dark matter experiment has been busted, and it‘s an
incredible success for the scientific method [29].
12. MOND
Dark matter is not an unreasonable explanation for our observations, but it‘s not the
only possible explanation for galaxies‘ behavior. You can, for instance, modify the
law of gravity. Many of these alternatives, called Modified Newtonian Dynamics
(MOND). An alternative to Dark Matter is to explain the missing mass by means of
modification of gravity at large distances or more specifically at small accelerations.
There have been suggestions that the law of gravity could be different over galactic
scales and could perhaps resolve the problem of Dark Matter implied by flat rotation
curves. A 1/r force law, rather than an inverse square law for gravity, is easily seen to
imply a flat rotation curve for all galaxies, i.e. v is constant. MOND is a modification
of Newtonian mechanics rather than Newtonian gravity. In 1983, Morderhai Milgrom
proposed phenomenological modification of Newton‘s law which fits galaxy rotation
curves. The theory, known as Modified Newtonian Dynamics (MOND) automatically
recovers the Tully-Fischer law. Apart from flat rotation curves, evidence for dark
matter comes from the small anisotropies in the cosmic microwave background
radiation(CMBR), which suggests that forming large scale cosmic structures on time
scales shorter than the Hubble time essentially requires substantial amount of
gravitating cold dark matter. The idea is that below a certain (minimal) acceleration
empirically chosen as 0=1010 2 [30]. The theory modifies the acceleration of
a particle below a small acceleration 0=1010 2. This therefore enters the
theory as a universal constant. The gravitational acceleration at large distances then
reads =0
at large distances, instead of the Newtonian =
.
There are two main difficulties with MOND. First, it does not explain how galaxy
clusters can be bound without the presence of some hidden mass. Second, attempts to
derive MOND from a consistent relativistic field theory have failed. One such attempt
is the Tensor-Vector-Scalar. Many models are unstable or require actions which
depend on the mass M of the galaxy, thereby giving a different theory for each galaxy.
Moreover modified gravity theories have serious difficulties reproducing the CMB
power spectrum. Modified gravity theories can give an excellent phenomenological fit
through an adjustment of the values of the extra parameters, but there is no universal
principle to determine these values. This requirement for simplicity and predictivity is
met by General Relativity. The modifications of gravity proposed as alternative to the
Dark Matter paradigm illustrate the need for tests of GR at large distances and low
accelerations. In modified gravity, dark matter is not made of particles. Instead, the
gravitational pull felt by normal matter comes from a gravitational potential that is not
the one predicted by general relativity. In general relativity and its modifications
likewise, the gravitational potential is described by the curvature of space-time and
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 53-72 www.itspoa.com/journal/er
encoded in what is called the ―metric.‖ In the versions of modified gravity studied in
the new paper, the metric has additional terms which effectively act on normal matter
as if there was dark matter, even though there is no dark matter [31]. However, the
metric in general relativity is also what gives rise to gravitational waves, which are
small, periodic disturbances of that metric. If dark matter is made of particles, then the
gravitational waves themselves travel through the gravitational potential of normal
plus dark matter. If dark matter, however, is due to a modification of the gravitational
potential, then gravitational waves themselves do not feel the dark matter potential.
The presence of the gravitational potential increases the run-time of the signal, and the
deeper the potential, the longer the run-time. This is known as ―Shapiro-delay‖ and is
one of the ways, for example, to probe general relativity in the solar system. The
Shapiro-delay on the Sun is about 10-4 seconds. If you scale this up to the Milky Way,
with a mass of about 1012 times that of the Sun, this gives 108 seconds, which is
indeed about a year or so. You gain a little since the dark matter mass is somewhat
higher and lose a little because the Milky Way isn‘t spherically symmetric. But by
order of magnitude this simple estimate explains the constraint. The paper hence rules
out all modified gravity theories that predict gravitational waves which pass
differently through the gravitational potential of galaxies than electromagenetic waves
do. The recently reported gravitational wave detection, GW170817, was accompanied
by electromagnetic radiation. Both signals arrived on Earth almost simultaneously,
within a time-window of a few seconds. The observation is difficult to explain with
some variants of modified gravity because in these models electromagnetic and
gravitational radiation travel differently. This is a big problem for some alternatives
to dark matter (such as Bekenstein‘s TeVeS and Moffat‘s Scalar-Vector-Tensor
theory) as this new paper lays out: GW170817 Falsifies Dark Matter Emulators [32].
The stumbling block has been to figure out the underlying physical reason for the new
law. This is actually a big ask. In a 3D universe with a flat space-time, conservation of
energy and momentum automatically gives forces like gravity and electrostatics
a spatial dependence (the force falls as the square of the distance). These laws are a
consequence of the nature of the Universe, so changes to the laws also have to be
down to the fundamental nature of the Universe. The Universe doesn't have a
completely flat space-time, though. Instead space-time warps and flows around
massive objects; which provides alternative theories of gravity, a new class of
theoretical gravities. For the versions of MOND, the basic idea is this: there is no dark
matter, but there are two different metricsmetrics are spacetimes coupled to matter.
One metric is coupled to ordinary matter. Gravitational waves, on the other hand,
have an entirely different metric that, is warped out of shape. Its warped shape is what
we perceive as dark matter. So there is no dark matterinstead the spacetime is
naturally warped in the absence of dark matter. These two seemingly independent
metrics can explain the structures of galaxies and of collisions between galaxy
clusters, but the idea has consequences. For instance, if a something should emit both
gravitational waves and light, the two waves will travel by different paths depending
on the masses they encounter. So, light and gravitational waves won‘t arrive at a
distant observation point at the same time. When two neutron stars spiraled into each
other and merged, they released a huge amount of energy as both light and
gravitational waves. The light and the gravitational waves travel along the direct line
of sight to us, curling around the gravity wells of intervening galaxies along the way.
As a result, the initial burst of light and gravitational waves hid a little gem: the time
difference between the arrival of the gravitational waves and the light. All 1.7 seconds
of it [33]. The measured delay was so much shorter than the difference predicted
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 54-72 www.itspoa.com/journal/er
by double metric theories. Yes, that was the recorded delay between the two signals.
This is a dead MOND theory [34]. Mond deals with gravity as force that should be
decelerate at extended regions. Contradicts the concept of gravity as a curvature in
General Relativity Theory: Gravity introduces nothing locally. All the effects of
gravity are felt over extended regions of spacetime. A new relativistic theory for
modified Newtonian dynamics by Constantinos Skordis and Tom Złosnik: We
discuss phenomenological requirements leading to its construction and demonstrate
its agreement with the observed Cosmic Microwave Background and matter power
spectra on linear cosmological scales”[35].
13. F(R) Gravity
F(R) gravity [36] is a type of modified gravity theory which generalizes Einsteins
general relativity. F(R) gravity is actually a family of theories, each one defined by a
different function f of the Ricci scalar R. The simplest case is just the function being
equal to the scalar; this is general relativity. As a consequence of introducing an
arbitrary function, there may be freedom to explain the accelerated expansion and
structure formation of the Universe without adding unknown forms of dark energy or
dark matter. Some functional forms may be inspired by corrections arising from a
quantum theory of gravity. F(R) gravity was first proposed in 1970 by Hans Adolph
Buchdahl. It has become an active field of research following work by Starobinsky on
cosmic inflation. A wide range of phenomena can be produced from this theory by
adopting different functions. F(R) is a class of effective theories representing a new
approach to the gravitational interaction. The paradigm is that Einstein's General
Relativity has to be extended in order to address several shortcomings emerging at
ultraviolet and infrared scales. These are essentially due to the lack of a final, self-
consistent theory of quantum gravity. From the astrophysical and cosmological
viewpoints, the goal is to encompass phenomena like dark energy and dark matter
under a geometric standard related to the possibility that gravitational interaction
depends on the scales. This geometric view, in principle, does not need the
introduction of further particle ingredients and preserves all the well-posed results of
General Relativity, being based on the same fundamental principles (Equivalence
Principle, diffeomorphism invariance, gauge invariance, etc.). The main criticism to
this approach is that, until now, no f(R) model, or any Extended Theory of Gravity,
succeeds in addressing the whole phenomenology ranging from quantum to
cosmological scales. Besides, the f(R) description of dark side of the universe is
substantially equivalent to that related to the hypothesis of dark material constituents.
However, many functional forms can now be ruled out on observational grounds, or
because of pathological theoretical problems. The need of one or more than one
experiment capable of retaining or ruling out one of the two concurring pictures, is
pressing to solve the debate [37].
14. Trajectory Through a Flat Space
Virial theorem (V=√(MG/r) fails to predict Mercury‘s orbit where the gravitational
field (curvature) is very strong near the sun and consequently the spacetime is not flat.
Virial theorem fails to valid throughout the entire Solar system. Why we assumed it
should be valid over the large structure spacetime of the galaxy and the cluster of
galaxies? We need a rigorous mathematics to generalize the domain of applicability of
the Virial theorem to cover the large structure scale. According to the Equivalence
Principle, it's impossible to detect the gravitational field (curvature) locally. The
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 55-72 www.itspoa.com/journal/er
imprint of the curvature is noticeable and significant over the large structure
spacetime. Virial theorem is valid only for flat space and fails to be valid for non-
Euclidean spacetime. Hence the discrepancy between the mass of the galaxy due to its
brightness and that due to its rotation velocity is due to the failure of applying Virial
theorem at large structure non-Euclidean spacetime of the galaxy to detect its mass.
Our main mistake is that we accept an unverifiable assumption that the portion of the
universe which can be observed is representative of the whole, and that the laws of
physics are the same throughout the whole universe. It is an oversimplification to
generalize that the universe is globally flat and the laws of physics are the same
throughout the whole universe. Newton`s laws of gravity do no longer hold in non-
Euclidean geometry. Einstein profited also of ideas earlier put forward by Riemann,
who stated that the Universe should be a curved manifold, and that its curvature
should be established on the basis of astronomical observations. The discovery of the
cosmic microwave background, the quantitative predictions in nucleosynthesis, the
emergence of dark matter and dark energy, the understanding of initial conditions and
structure formation in terms of an inflationary theory have marked the birth of
cosmology as a science and characterized its discovery phase. This was followed by
an extensive program in observational cosmology (precision studies of the cosmic
microwave background, large-scale surveys, gravitational lensing, telescopes from
radio to gamma rays), which proclaimed CDM as the standard model of cosmology
and which can be identified with the phase of consolidation. ―We are confronted with
the need to reconsider the guiding principles that have been used for decades to
address the most fundamental questions about the physical world. These are
symptoms of a phase of crisis. And yet, this superb monument of knowledge is
insufficient to address some fundamental questions. The Standard Model is incapable
of shedding light on the dynamics underlying electroweak symmetry breaking or
explaining the structure of quarks, leptons, and their mass pattern at a fundamental
level. The theory of inflation, in spite of its stunning conceptual successes, could not
be linked univocally with a unified theory of particle physics. Moreover, the
ubiquitous phenomenon of eternal inflation has changed the perspective on the
outcome of an inflationary universe and its properties. We have plausible explanations
for the cosmic baryon asymmetry, but we lack any conclusive empirical confirmation.
The nature of dark matter is still unknown. The observed value of the cosmological
constant is hard to reconcile with the rules of effective field theory, and quantum
gravity is still beyond our grasp. None of these problems are new, and theoreticians
have been tackling them for decades. What is changing is the feeling that the
paradigm that so successfully led to the Standard Model may not be the right tool to
make further progress. There is a widespread sensation that the organising principles
based on symmetry and separation of scales, which follow from an effective quantum
field theory approach, in spite of their triumphs, must be superseded by new
organising principles. Physicists are in search for new conceptual paradigms, which is
another symptom of a phase of crisis. Crisis means the opportunity to look at a
problem with new eyes; it is a moment of change, a discontinuity between past and
future. Crisis does not mean a decline of ideas, but the search for a paradigm
change‖[38]. Assuming flat space and circular orbit, astronomers use the Virial
theorem to determine the masses of the galaxies
21M V R G
M is the mass of the galaxy, V is the speed of the galaxy, R is the distance of the
galactic center and G is the gravitational constant.
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 56-72 www.itspoa.com/journal/er
Rotational Velocity: Using the power of the Doppler Shift, scientists can learn much
about the motions of galaxies. They know that galaxies rotate because, when viewed
edge-on, the light from one side of the galaxy is blue shifted and the light from the
other side is red shifted. One side is moving toward the Earth, the other is moving
away. They can also determine the speed at which the galaxy is rotating from how far
the light is shifted. Knowing how fast the galaxy is rotating, they can then figure out
the mass of the galaxy mathematically. As scientists look closer at the speeds of
galactic rotation, they find something strange. The individual stars in a galaxy should
act like the planets in our solar system, the farther away from the center, the slower
they should move. But the Doppler Shift reveals that the stars in many galaxies do not
slow down at farther distances. And on top of that, the stars move at speeds that
should rip the galaxy apart; there is not enough measured mass to supply the gravity
needed to hold the galaxy together. These high rotational speeds suggest that the
galaxy contains more mass than was calculated. Scientists theorize that, if the galaxy
was surrounded by a halo of unseen matter, the galaxy could remain stable at such
high rotational speeds. Another method astronomers use to determine the mass of a
galaxy (or cluster of galaxies) is simply to look at how much light there is. By
measuring the amount of light reaching the earth, the scientists can estimate the
number of stars in the galaxy. Knowing the number of stars in the galaxy, the
scientists can then mathematically determine the mass of the galaxy. Astronomers use
the Mass Luminosity equation to determine the mass of a star:
42ML
M = the star‘s mass. L = the star‘s Luminosity. Fritz Zwicky used both methods
described here to determine the mass of the Coma cluster of galaxies over half a
century ago. When he compared his data, he brought to light the missing mass
problem. The high rotational speeds that suggest a halo reinforce Zwicky‘s findings.
The data suggest that less than 10% of what we call the universe is in a form that we
can see. Now scientists are diligently searching for the elusive dark matter, the other
90% of the universe.
Figure 5. In the Euclidean geometry space is divided into cubes and one experiences the ordinary,
familiar perspective: the apparent angular size of objects is proportional to the inverse of their
distance [39].
Hyperbolic spacetime and hyperbolic trajectory, not dark matter, can resolve the
discrepancy between the flat rotation curves of stars within a galaxy and the rotation
curves expected from Kepler‘s third law. The orbital velocity ( ) of a body traveling
along hyperbolic trajectory in flat space- can be computed as Vallado theorem [40]:
2 1 3V r am
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 57-72 www.itspoa.com/journal/er
Where:
m
is standard gravitational parameter,
r is radial distance of orbiting body from central body
a is the negative semi-major axis.
According to Newton‘s law of gravity the orbit of Mercury around the sun should
be a perfect ellipse with the sun at one focus. That's just Kepler‘s first law. Mercury
was not precisely following its predicted orbit. The sun has the strongest gravitational
field of any object in the solar system. Since, according to general relativity the
curvature of space-time is a direct measure of the strength of a gravitational field. As
Mercury tries to move along an elliptical orbit, the orbit itself slowly moves. This
effect called the precession of Mercury‘s perihelion. The gravity near the sun is strong
enough to warp space-time. Far away from the sun the space-time turns flat, the other
planets obey Keplerian elliptical orbit. The same analogy can be applied to describe
the trajectory of a galaxy within the hyperbolic space-time of its parent cluster. The
hyperbolic space-time causes the galaxy to speed up as moved away from the center.
Far away from the center the space-time returns flat, while one could apply Vallado
theorem for the hyperbolic trajectory in the flat space-time. The body traveling along
hyperbolic trajectory will attain at infinity an orbital velocity called hyperbolic excess
velocity
that can be computed as:
4Vam

Gmm
is standard gravitational parameter, a is the negative semi-major axis of
orbits hyperbola. Kepler‘s third law and consequently Virial theorem does no longer
hold for Non-Euclidian space. In the hyperbolic space-time, galaxies furthest away
from the center are moving fastest until they reached large distance from the center
the space-time return flat. They possessed hyperbolic trajectory, according to Vallado
theorem, with constant speed, called hyperbolic excess velocity,
Vam

(the
flat curve)
Figure 6. Hyperbolic space shown here is tiled with regular dodecahedra. In Euclidean space
such a regular tiling is impossible. The size of the cells is of the same order as the curvature scale.
Although perspective for nearby objects in hyperbolic space is very nearly identical to Euclidean
space, the apparent angular size of distant objects falls off much more rapidly, in fact
exponentially, as can be seen in the figure [39].
15. The Hyperbolic Geometry of the Universe
The dynamical equations of cosmology (Friedmann‘s equation, G=c=1):
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 58-72 www.itspoa.com/journal/er
22
22
85
3
2 8 (6)
R k R
RR R k pR
pr
p

Where R is the scale factor,
r
is the energy-density, p is the pressure and k is the
curvature. Now we shall solve the differential equation (1) by separating the variables.
We assume the Big Bang Model as an initial condition (i.e. R=0 when t=0).
22
22
2
83
2
83
28
383
(8 / 3)
(8 / 3)
()
/ ( )
/k
R k R
R R k
R R k
dR R k dt
dR R dt
pr
pr
pr
pr
pr
pr





Differential equation (1) allows one to deal with ρj as a parameter since it's not an
explicit function of t , so Eq. (1) can be solved for any chosen fixed value, ρj from
the stream of the various values of the parameter ρ
12
, ,..., ,..., ,..., ,...
planck j now
r r r r r
By means of the mean value theorem, we assume approximately that ρj evolves to
the fixed physical value ρj exactly simultaneously associated to the state (tj , Rj)
ρj varies as j varies. We get
11
jj
cosh ( / 3 /8 ) cosh 0 8 /3 (7)R k tpr pr


Now we use complex analysis as follows: .
12
11
1
1
cosh ln( 1)
cosh 0 ln 1 ln 1, , cosh 0 ln 1
cosh 0 (1 2)ln( 1),
cosh 0 ln( 1) (1 2)ln( 1)
x x x
or
or


1
1
1
ln( 1)
cosh 0 2 ,
cosh 0 3 2
i
e
i
i or
i
p
p
p
p


Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 59-72 www.itspoa.com/journal/er
Substitute the first value
1
cosh 0 2ip
in equation (7), we get:
jj
j j j
j j j
jj
( ) 3 /8 .cosh( 8 /3 /2)
( ) 3 /8 .(cosh 8 /3.cosh( /2) sinh( /2).sinh 8 /3)
( ) 3 /8 .(cosh 8 /3.cos( /2) sin( /2).sinh 8 /3)
( ) 3 /8 .sinh 8 /3
R t k t i
R t k t i i t
R t k t i t
R t i k t
pr pr p
pr pr p p pr
pr pr p p pr
pr pr



Since the function
tr
is always positive, so is any chosen fixed value
j
r
. A simple
analysis shows that the R(t) scale solution represented in the last equation is complex
if k is positive, negative if k is negative and vanishes if k is zero. So the first
value
1
cosh 0 2ip
is rejected. Substitute the other value
1
cosh 0 3 2ip
in equation
(7), we get,
jj
j j j
j j j
jj
( ) 3 /8 .cosh( 8 /3 3 /2)
( ) 3 /8 (cosh 8 /3.cosh(3 /2) sinh(3 /2)sinh 8 /3)
( ) 3 /8 (cosh 8 /3.cos(3 /2) sin(3 /2)sinh 8 /3)
( ) 3 /8 sinh 8 /3
R t k t i
R t k t i i t
R t k t i t
R t i k t
pr pr p
pr pr p p pr
pr pr p p pr
pr pr




R(t), the scale factor solution in the last equation is real, positive and non-vanishing
if and only if k is negative. Since k is normalized, substitute k =-1, in the last equation,
we get,
jj
jj
jj
jj
( ) 3 /8 sinh 8 /3
( ) 3/8 sinh 8 /3
( ) . 3/8 sinh 8 /3
( ) 3/8 sinh 8 /3 (8)
R t i k t
R t i t
R t i i t
R t t
pr pr
pr pr
pr pr
pr pr


Which mean that R(t)either vanishes if k = 0 or it is complex if k =1. Thus, the
curvature k must be negative and consequently the universe must be hyperbolic and
open [41].The current observed density of the Universe
r
=10-31 g/cm3, consistent
with a hyperbolic open universe.
Note that the solution represented by Eq. (8) is evaluated only for the values
simultaneously associated with
j
r
, namely
,
jj
Rt
3/8 sinh 8 /3 9
j j j j
Rtpr pr
Verification: The above scale factor can be verified even at the Planck scale and the
current scale as follows:
(i))Planck scale: Substitute a given Planck time and Planck density in equation
(9), while we assume Planck length is unknown. Note that in geometrical units:-
The speed of light c = 1
1 sec = 2.997×1010cm
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 60-72 www.itspoa.com/journal/er
1 gram = 7.425×10-29cm
1 eV = 1.324×10-61cm.
We have Planck scale from the following
Planck time = 5.4×10-44s
Planck length = 1.62×10-33cm
Planck mass = 1.2×1025eV/c2
Planck density = M/V = M/L3 = 1.2×1025(eV/c2)/(1.6×10-33)3
=1.2×1025(1.324×10-61cm)/(1.6×10-33)3=3.8789×1062cm-2
(ii) The current scale
Note that in geometrical units
1 sec = 2.997×1010cm
1 gram = 7.425×10-29cm
1 yr = 3.16×107 s
The energy density now =10-31 g/cm3 =7.425×10-60cm-2
The age of the Universe =14×109 yr= cm
Substitute the above data in the hyperbolic time evolution equation of the Universe
(9), yields
The predicted calculated value agrees with the observable value.
now
r
now
t
28
1.32587 10
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 61-72 www.itspoa.com/journal/er
Figure 7. The Cosmic Table. The current observed universe 1.3×1028cm [42].
16. Equation of the Radial Motion in the Galaxys Hyperbolic
Spacetime
To seek completeness, it remains to develop an equation of motion describes the
speed up motion in the hyperbolic space-time and predicts the flat rotation curve. To
do this, I will follow the following strategy
1. Seek for an equation
v f r
such that ,
that satisfies the Newtonian limit far from the center:
2.
3. I guess the required equation that fits the data- should be
4. The final step in the mathematical problem solving method is to prove the
conjecture
To find such an equation of the radial motion in the galaxys hyperbolic space-time,
we proceed as follows: The required modified Schwarzschild spherically symmetric
metric will be
For which the Schwarzschild metric is just an approximation
The Ricci tensor [43]:
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 62-72 www.itspoa.com/journal/er
From
0
tt
RR
qq

we have
0nl


, so
knl
K is constant. Write simply,
log kln
. Equation (i) is now just
Equation (iii) is
Now we have the complete solution
For radial motion, . The Schwarzschild metric will be
The free fall from rest of a star (of mass m and energy E) far from the center
possesses [44],
To our purpose for the hyperbolic spacetime, the velocity far away from the center
would be
Vam

and consequently
1kam
Neglect the term
2
2rm
and rearrange
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 63-72 www.itspoa.com/journal/er
(10)
Example (1)
A typical galaxy of ordinary enclosed mass (Milky Way or Andromeda) [45],
16 2 16
16 2 16 2
2
4.5 10 1 3.1 10
9 10 1 3.1 10 210
1.45 2.9 210
2
r kpc
km s km s r km
km s km s r km
rr
V e r kpc a
Ve
Ve
mmm



The graph of the last equation is plotted by Visual Mathematics Program as follows
Figure 8.The curve describes the motion of a star in the Milky way (or Andromeda) galaxy. The
vertical axis represents the velocity, while the horizontal axis represents the distance from the
center of the galaxy. [46].
elpmaxE (2)
A typical cluster of galaxies of ordinary enclosed mass
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 64-72 www.itspoa.com/journal/er
14 14 30
14 30 31
14
14 5
19 2
10 10 2 10
10 2 10 7.4 10
1.5 10
1.5 10 3 10
4.5 10
M M kg
km
km
km km s
km s
m
m
m
m


2
1000
1000
a
a
m
m


19 19
()
4.5 10 3.1 10 2
19 19
2
1.45
2 ( )
2 4.5 10 3.1 10 1000
2.9 1000
r pc
r
r
V e r pc a
V e r km s
V e r
mmm


The graph of the last equation is plotted by Visual Mathematics Program as follows
Figure 9. The curve describes the motion of a cluster of galaxies. The vertical axis represents the
velocity, while the horizontal axis represents the distance from the center of the cluster [46].
The dark matter halo is nothing but instead of it we have a cell of same hyperbolic
negative curvature as the negative curvature of the whole Hyperbolic Universe. Virial
theorem
2
M V R G
does no longer hold for Non-Euclidian space. We developed the
equation of motion in the hyperbolic space-time:
21
r
V e r a
mm

, that
describes the speed up motion in the hyperbolic space-time and predicts the flat curve.
Farther away from the center the exponential factor
1r
e
drops to one. Galaxies
furthest away from the center are moving fastest until they reached large distance
from the center the space-time turns flat and they possessed hyperbolic trajectory:
21V r am
, according to Vallado theorem, with constant speed called hyperbolic
excess velocity:
Vam

that can explain the galaxy flat rotation curve problem, a
is the negative semi-major axis of orbits hyperbola.
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 65-72 www.itspoa.com/journal/er
17. The Hyperbolic Equation Of Motion Predicts UDGs Rotation
Curve
UDGs are low surface brightness galaxies, with an extended light distribution. At
fixed stellar mass (or luminosity) they have significantly larger effective radii than the
classical dwarf galaxy. They have fewest stars thousand stars fewer than typical size
galaxy like our Milky Way. UDGs stellar mass is 10-100 order less than typical size
galaxy like our Milky Way[47]. The two galaxies, called NGC 1052-DF2 and NGC
1052-DF4 are the size of the Milky Way but contains just 1 percent of our galaxy‘s
stars. The two galaxies are very faint and far away from Earth [48,49]. Astronomers
have found yet another ghostly galaxy that appears to be devoid of dark matter. Pavel
E. Mancera Piña of the University of Groningen in the Netherlands, a member of the
team that studied AGC 114905. This latest object, known as AGC 114905, is similar
in size to our own spiral galaxy yet has 1,000 times fewer stars[50]. The observation
suggests that there is no room for dark matter,‖ Mancera Piña says. But the newfound
object AGC 114905 adds an entirely new twist to this complex cosmic tale. In 2020
Mancera Piña and his colleagues reported their discovery of six ultradiffuse gas-rich
galaxies[51]. The VLA observations revealed that gas clouds in these galaxies are
orbiting much slower than would be expected if the galaxies harbored typical amounts
of dark matter. Also, unlike the pair of DF2 and DF4, each of these galaxies is a
singleton, isolated and nowhere near any other cosmic object that could strip away
dark matter. If the dark-matter-free status of AGC114905 is ever confirmed,
cosmologists will be forced to reexamine and perhaps even abandon some of their
most cherished theories. We show that our hyperbolic equation of motion predicts the
kinematics of the UDGs and traces their speed rotation curves.
Figure 10. Surface density mass of AGC 114905[52].
The latest observations of AGC 114905 also disagree with predictions from
theories of modified gravity, such as modified Newtonian dynamics (MOND)[53].
Such theories seek to explain the motions of stars and gas in galaxies without
resorting to dark matter. ―[MOND] tells you directly how the galaxy should rotate,‖
Mancera Piña says. ―And this prediction is completely off of our value.‖[52]
Figure 11. Mond prediction (green line) of the circular speed of AGC 114905 (red points). The
baryonic circular speed profile in a magenta line.[52]
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 66-72 www.itspoa.com/journal/er
Example (3)
A typical UDG Galaxy with mass fewer than the mass of the Milky Way by one
order Mbar =(1.4)1010 Mʘ. Disc rotating speed is Vc=23 km/s. The velocity dispersion
is 5km/s, accordingly its equation of motion will be
The graph of the last equation is plotted by Visual Mathematics Program as follows:
Figure 12. Atypical UDG (1.4)1010 Mʘ. Vertical axis: Circular speed (1=10km/s). Horizontal
axis: Radius (1=kpc)
Example (4)
The baryonic mass of AGC 114905 is: Mbar =(1.4).109Mʘ, which is hundredth
fewer than the mass of the Milky Way (by two orders), accordingly the equation of
motion of AGC 114905 will be
The graph of the last equation is plotted by Visual Mathematics Program as follows
Figure 13. AGC 114905 UDG (1.4)109 Mʘ. Vertical axis: Circular speed (1=10km/s).
Horizontal axis: Radius (1=kpc).
Example (5)
A typical UDG Galaxy with mass thousand fewer than the mass of the Milky Way
(by three orders): Mbar =(1.4)108 Mʘ, [54] accordingly its equation of motion will be
Figure 14.Atypical UDG (1.4)108 Mʘ. Vertical axis: Circular speed (1=10km/s). Horizontal axis:
Radius (1=kpc).
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 67-72 www.itspoa.com/journal/er
18. Conclusions
- Dark Matter has to exist to explain for instance the discrepancy between the flat
rotation curves of stars within a galaxy and the rotation curves expected from Keplers
third law.
-MACHOs, Attractive Dark Mater particles, including WIMPs have ruled out.
Supersymmetric particles have not been detected.
-Time passes without a confirmed detection, even the most heavily backed theories
are beginning to look less likely. A series of experiments have systematically searched
for, and failed to find, the theoretical candidates for dark matter. Scientists from two
of the world‘s biggest dark matter detectors (XENON1T and PandaX-II
collaborations) have reported that their latest experiments, like all earlier attempts,
have produced no sign of the elusive substance. Combined with negative results from
American LUX experiment and tests at the Large Hadron Collider, these results are
adding to a sense of frustration among researchers. There is a widespread view that
many of the most theoretically attractive candidates for dark matter should have been
detected by now, based on their predicted properties. In the absence of such a
discovery, the field has begun to redirect efforts toward new, and sometimes very
different, ideas.
-MOND is almost ruled out. The paper arXiv: 1710.06168 rules out all modified
gravity theories that predict gravitational waves which pass differently through the
gravitational potential of galaxies than electromagnetic waves do.
-f(R) gravity: is a type of modified gravity theory which generalizes
Einstein'sgeneral relativity. The main criticism to this approach is that, until now, no
f(R) model, or any Extended Theory of Gravity, succeeds in addressing the whole
phenomenology ranging from quantum to cosmological scales. Besides, the f(R)
description of dark side of the universe is substantially equivalent to that related to the
hypothesis of dark material constituents. However, many functional forms can now be
ruled out on observational grounds, or because of pathological theoretical problems.
-Virial theorem (V=√(MG/r) fails to predict Mercury‘s orbit where the gravitational
field (curvature) is very strong near the sun and consequently the spacetime is not flat.
Virial theorem fails to be valid throughout the entire Solar system. According to the
Equivalence Principle, it‘s impossible to detect the gravitational field (curvature)
locally. The imprint of the curvature is noticeable and significant over the large
structure spacetime. Virial theorem is valid only for flat space and fails to be valid for
non-Euclidean spacetime. Hence the discrepancy between the luminous mass of the
galaxy and the rotation velocity‘s mass is due to the failure of applying Virial theorem
at large structure non-Euclidean spacetime of the galaxy to detect its mass. Our main
mistake is that we accept an unverifiable assumption that the portion of the universe
which can be observed is representative of the whole, and that the laws of physics are
the same throughout the whole universe. It is an oversimplification to generalize that
the universe is globally flat and the laws of physics are the same throughout the whole
universe. Newton`s laws of gravity do no longer hold in non-Euclidean geometry.
-It‘s important that we don‘t put all our eggs in one cosmological basket, as Avi
Loeb, Chair of Astronomy at Harvard, has recently warned. In Loeb‘s words: ―To
avoid stagnation and nurture a vibrant scientific culture, a research frontier should
always maintain at least two ways of interpreting data so that new experiments will
aim to select the correct one. A healthy dialogue between different points of view
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 68-72 www.itspoa.com/journal/er
should be fostered through conferences that discuss conceptual issues and not just
experimental results and phenomenology, as often is the case currently‖[55].
-Dwarf galaxies dont fit standard model The model predicts that dwarf galaxies
should form inside of small clumps of dark matter and that these clumps should be
distributed randomly about their parent galaxy‖and challenges cold dark matter
cosmology that the Dwarf galaxies should ―preferentially oriented
alignment.‖Standard model fails to replicate what's observed and therefore they seek
alternative.
-(CMB), which suggests that forming large scale cosmic structures on time scales
shorter than the Hubble time essentially requires substantial amount of gravitating
cold dark matter. Such speculative scenario is not well supported mathematically.
Most early massive galaxies are strongly dominated by normal matter ruled out the
speculations that the Theory of large scale structure formation requires anisotropies
in the CMB, but also requires the presence of dark matter in early universe.One can
infer the Hubble constant from the size of the largest fluctuations seen in the CMB.
The distance ladder being model-independent and the CMB being model-dependent.
The discrepancy in the value of Hubble constant measured by the two methods
shocks the CMB model.
- Anti-matter was well defined before we focus observation to detect it. Nothing we
knew about Dark Matter neither its construction nor its constituents. What should we
observe? Unless a theoretical description exists to visualize Dark Matter, our quest
would be hopeless.
-Simeon Bird, one of the physicists at Johns Hopkins says : “When you dont know
what something is, you have to consider everything. But even nondetections
constitute progress, in that they reveal to us what the dark matter is not!!! Does this
make sense, to rule out what is not dark matter? Potato is not dark matter and tomato
also is not dark matter …etc indefinitely. Do dark matter particles constitute a
scientific theory? Should we wait until we knew what the Dark Matter is not? By this
sense, could Dark Matter particles be falsifiable?
-However, if the cluster‘s spacetime is not flat; the lensing could be interpreted as a
curved spacetime,not via the existence of Dark Matter.The missing mass required to
account for the observed lens is the same as the missing mass required to account for
the observed flat rotation curve. The hyperbolic spacetime curvature not Dark
Matter- accounts for such a missing mass.
-Virial theorem does no longer hold for Non-Euclidian space. In the hyperbolic
space galaxies furthest away from the center are moving fastest according to the
equation
-We modify the equation of motion in the hyperbolic spacetime
21
r
V e r a
mm

We derived the modified the equation of motion in the hyperbolic spacetime, by
modifying Schwarzschild metric in the hyperbolic spacetime. Its clear, far away from
the centre of mass the limit of the modified equation of motion in the hyperbolic
spacetime would be the Newtonian hyperbolic equation of motion in flat space
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 69-72 www.itspoa.com/journal/er
That predicts the flat rotation curve without need for dark matter.
-We show that our hyperbolic equation of motion predicts the kinematics of the
UDGs and traces their speed rotation curves
- The hyperbolic structure of the spacetime, not dark matter, warps the galaxys
spacetime and accounts for the current anomalies (The galactic dynamics, the CMB
anisotropies and the gravitational lensing) in the observations.
-Our model agrees with observations and accounts for the flat rotation curve.
Compared with other models, our model seems to be aesthetically pleasing and
preferred according to the Criteria for scientific method and Occams razor.
-Criteria for scientific method:
(i). The model must fit the data and agree with observations.
(ii). The model must make predictions that allow it to be tested (falsifiable).
(iii). The model should be aesthetically pleasing (Occams razor: If you have two
theories that both explain the observed facts, then you should use the simplest with the
fewest assumptions).
Conflicts of Interest
The author declares that there is no conflict of interest regarding the publication of
this article.
Funding
This research received no specific grant from any funding agency in the public,
commercial or not-for-profit sectors.
References
[1] Mary-Ann Russon International Business Times February 13, 2017. Available onl
ine: https://blogs.scientificamerican.com/guest-blog/vera-rubin-didnt-discover-da
rk-matter/(accessed on 3 September 2017).
[2] Cooperstock, F.I.; Tieu, S. Galactic Dynamics via General Relativity: A
Compilation and New Developments. Int.J.Mod.Phys. 2007, A. 22, 2293-2325.
arxiv.org/abs/astro-ph/0610370.
[3] Vladimir, L.; Paolo, C.; Nicola, V. Dark Matter In Cosmology. Int. J. Mod. Phys.
2014, A 29, 1443001, DOI: https://doi.org/10.1142/S0217751X14430015.
[4] Dark-matter. Available online: https://higgshunters.files.wordpress.com/2014/08/
dark-matter.jpg(accessed on 27 March 2017).
[5] Annual Reviews. Astron. Astrophys, 2010, 48, 673-710.
[6] Oliver, M.; Marcel, S.P.; Helmut, J.; Federico, L. A whirling plane of satellite
galaxies around Centaurus A challenges cold dark matter cosmology. Science,
2018, 359(6375), 534-537.
[7] Adam, G.R.; Lucas, M.M.; Samantha, L.H.; Dan, S.S.C.; Alexei, V.F.; Brad. E,T.;
Mark, J.Reid.; David, O.J.; Jeffrey, M.S.; Ryan, C.; Pete, C.; Yuan, W.L.; Peter,
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 70-72 www.itspoa.com/journal/er
J. B.; Ryan, J.A 2.4% Determination of the Local Value of the Hubble Constant.
arXiv:1604.01424 [astro-ph.CO].
[8] Wendy L. Freedman. Cosmology at a Crossroads: Tension With the Hubble Cons
tant. Available online: https://arxiv.org/ftp/arxiv/papers/1706/1706.02739.pdf(acc
essed on 27 March 2017).
[9] Massimo, M.; Guido, D.; Pietro, B. et al. An excess of small-scale gravitational
lenses observed in galaxy clusters.Science, 2020, 369(6509),1347-1351, DOI:
10.1126/science.aax5164.
[10] Wang, J.; Bose, S.; Frenk, C.S.; Gao, L.; Jenkins, A.; Springel, V.; White, S.D.M.
Universal structure of dark matter haloes over a mass range of 20 orders of
magnitude. Nature, 2020, 585, 39-42.
[11] Kevork N.A.; Shunsaku, H.; Manoj, K.; Ryan, E.K.; Oscar, M. Strong constraints
on thermal relic dark matter from Fermi-LAT observations of the Galactic Center.
Phys. Rev. D. 2020, 102, 043012.
[12] Kevork N.A.; Shunsaku, H.; Manoj, K.; Ryan, E.K.; Oscar, M. Strong constraints
on thermal relic dark matter from Fermi-LAT observations of the Galactic Center.
Phys. Rev. D. 2020, 102, 043012.
[13] Jeff, H. Dark Matter: What is the Matter?Nature, 2016, 537, S194-S197.
[14] Available online: http://finance.yahoo.com/news/11-wimpy-galaxies-beating-brig
htest-142400173.html(accessed on 27 March 2017).
[15] Tinney,C.G. The dark matter implications of brown dwarfs. In The Third Stromlo
Symposium.The Third Stromlo Symposium: The Galactic Halo, 1999, 165,419.
[16] Available online: https://www.nasa.gov/vision/universe/starsgalaxies/brown_dwa
rf_detectives(accessed on 27 March 2017).
[17] Neil, S.The Dark Universe. Nature, 2016, 537, S206.
[18] E. Aprile et al. (XENON Collaboration). First Dark Matter Search Results from
the XENON1T Experiment. Phys. Rev. Lett. 119, 181301.
[19] Available online: https://universe-review.ca/F01-introduction.html(accessed on
27 March 2017).
[20] Richard, H.The Dark Universe. Nature, 2016, 537,S193.
[21] Adam, G. Riess et al. A 2.4% Determination of the Local Value of the Hubble
Constant.2016, arXiv:1604.01424 [astro-ph.CO].
[22] Available online: https://www.yahoo.com/news/dark-matter-taking-over-universe
-181001851.html?.tsrc=daily_mail&uh_test=2_05(accessed on 20 March 2012).
[23] Vladimir, L.; Paolo, C.; Nicola, V. Dark Matter In Cosmology. Int. J. Mod. Phys.
A.2014, 29, 1443001, DOI: https://doi.org/10.1142/S0217751X14430015.
[24] Vladimir, L.; Paolo, C.; Nicola, V. Dark Matter In Cosmology. Int. J. Mod. Phys.
A.2014, 29, 1443001, DOI: https://doi.org/10.1142/S0217751X14430015.
[25] Oliver Müller, Marcel S. Pawlowski, Helmut Jerjen, Federico Lelli. A whirling
plane of satellite galaxies around Centaurus A challenges cold dark matter
cosmology. DOI: 10.1126/science.aao1858. arXiv:1802.00081v1 [astro-ph.GA].
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 71-72 www.itspoa.com/journal/er
[26] Sabine, H. The Bullet Cluster as Evidence against Dark Matter. Available online:
http://backreaction.blogspot.com/2017/01/the-bullet-cluster-as-evidence-against.h
tml (accessed on 11 November 2017).
[27] Jounghun and Eiichiro. Bullet Cluster: A Challenge to LCDM Cosmology.
Astrophysical Journal, 2010, 718, 60-65, DOI: 10.1088/0004-637X/718/1/60.
[28] M. Markevitch et al. The Matter of the Bullet Cluster. X-ray: NASA/CXC/CfA/.
Available online: https://apod.nasa.gov/apod/ap060824.html (accessed on 6 June
2018).
[29] Available online: https://www.forbes.com/sites/startswithabang/2021/03/04/good
bye-damalibra-worlds-most-controversial-dark-matter-experiment-fails-replicatio
n test/(accessed on 11 November 2017).
[30] Sivaram, C. Dark matter (energy) may be indistinguishable from modified gravity
(MOND). International Journal of Modern Physics D. 2017, 26, 1743010, DOI:
doi.org/10.1142/S0218271817430106.
[31] Sabine, H. New gravitational wave detection with optical counterpart rules out
some dark matter alternatives. arXiv:1710.06168 [astro-ph.HE]. Available online:
http://backreaction.blogspot.com/2017/10/new-gravitational-wave-detection-
with.html?spref=tw(accessed on 11 November 2017).
[32] Sibel, B.; Shantanu, D.; Emre, K.; Richard, W. GW170817 Falsifies Dark Matter
Emulators. Phys. Rev. D, 2018, 97, 041501. arXiv:1710.06168 [astro-ph.HE].
DOI: 10.1103/physRevD.97.041501.
[33] LIGO Scientific Collaboration, Virgo Collaboration, Fermi Gamma-Ray Burst
Monitor, INTEGRAL. Gravitational Waves and Gamma-rays from a Binary
Neutron Star Merger: GW170817 and GRB 170817A. arXiv:1710.05834 [astro-
ph.HE]. DOI: 10.3847/2041-8213/aa920c.
[34] arXiv.org, ID: 1710.06168v, 2017.
[35] Constantinos Skordis, Tom Złosnik, arX:iv2007.00082v1 [gr-qc]- 30 Jun 2020 .
[36] F(R)_gravity. Available online: https://en.wikipedia.org/wiki/F(R)_gravity(access
ed on 11 November 2017).
[37] F(R)_theories_of_gravitation. Available online: http://wwhtw.scholarpedia.org/ar
ticle/F(R)_theories_of_gravitation(accessed on 11 November 2017).
[38] Gian, F.G. The Dawn of the Post-Naturalness Era. arXiv:1710.07663
[physics.hist-ph]. DOI: https://doi.org/10.48550/arXiv.1710.07663.
[39] Available online: http://www.damtp.cam.ac.uk/research/gr/public/inf_lowden.ht
ml(accessed on 11 November 2017).
[40] Hyperbolic_trajectory. Available online: http://en.wikipedia.org/wiki/Hyperbolic
_trajectory(accessed on 1 September 2017).
[41] Salah, A.M. The hyperbolic geometry of the universe and the wedding of general
relativity theory to quantum theory. Physics Essays,2012, 25(1), 112-118.
[42] Available online: https://universe-review.ca/F01-introduction.html(accessed on
11 November 2017).
[43] M. Carroll. Spacetime and Geometry. Addison Wesley.2004; pp. 195. ISBN 0-
8053-8732-3.
Volume 6, Issue 1, 2022 ISSN: 2617-4553
DOI: https://doi.org/10.31058/j.er.2022.61004
Submitted to Energy Research, page 72-72 www.itspoa.com/journal/er
[44] Edwin, T.; John, W. 1st ed . Black Holes. Addison Wesley: USA.ISBN 0-20L-
38423-X. 2000; pp. 3-12.
[45] Chaisson, E.; McMillan, S. Astronomy Today, 6th ed. (Addison Wesley, Boston),
2008; pp. 749.
[46] S. A. Mabkhout, Phys. Essays, 2013, 26,422.
[47] Mancera Pina P.E.; et al., 2019b, 883, L33.
[48] Laporte et C.F.P.; Agnello A., Navarro J. F., 2019, MNRAS, 484, 245.
[49] Trujillo 1., et al. 2019, MNRAS, 486, 1192.
[50] Ghostly Galaxies Hint at Dark Matter Breakthrough. Available online:
https://www.scientificamerican.com/article/ghostly-galaxies-hint-at-dark-matter-
breakthrough/(accessed on 11 November 2017).
[51] Mancera Pina P. E., et al., 2020, MNRAS, 495, 3636.
[52] Pavel E. Marcera Pina et al. arXiv:2112.00017v2 [astro-ph.GA] 20 Dec 2021.
[53] Available online: https://www.scientificamerican.com/article/dark-matter-may-be
-missing-from-this-newfound-galaxy-astronomers-say/?fbclid=IwAR297Pknmnk
La2kvYX2YcqUbWB65Wb7rxS3UrSUSD64gFliaTjV3hNCI2zM(accessed on 1
1 November 2017).
[54] Bershady, M.A.; Verheijen, M.A.W.; Westfall, K.R.; Swaters, R.A.; Martinsson.
The DiskMass Survey. IV. The Dark-matter-dominated Galaxy UGC 463. The
Astrophysical Journal, 2011, 742(1), 18.
[55] Available online: https://www.dal.ca/faculty/science/news events/news/2017/09/1
5/the_conversation__can_we_ditch_dark_energy_by_better_understanding_gener
al_relativity_.html(accessed on 11 November 2017).
© 2022 by the author(s); licensee International Technology and
Science Publications (ITS), this work for open access publication is
under the Creative Commons Attribution International License (CC
BY 4.0). (http://creativecommons.org/licenses/by/4.0/)
... The discrepancy in the value of Hubble constant measured by the two methods shocks the CMB model and consequently its presumed Dark Matter`s initial condition in the early universe. A mathematical discrepancy in the expansion rate of the Universe is now -pretty serious‖, and could point the way to a major discovery in physics, says a Nobel laureate; Prof Riess [7]. Finally, the value of the Hubble constant may be determined indirectly from CMB data through the use of the ΛCDM model itself.CMB highly dependent on the assumed energy content of the universe. ...
Article
The galactic dynamics, the CMB anisotropies and the gravitational lensing do not agree with the observations. Either an additional component of mysterious unseen nonbaryonic matter (Dark Matter) is needed-to bridge the gap between theory and observations-or, the theory of gravity should be modified. We prove the spacetime is hyperbolic. The problems with dark matter-or rather, the cases where cold, collisionless dark matter makes predictions that conflict with observations-almost exclusively occur on small cosmic scales: scales of large individual galaxies and smaller. It's true: certain modifications to gravity can better match the observations on these scales. All the experiments performed to detect Dark Matter were failed. The large structure spacetime is no longer flat. Hence the laws valid at flat space (e.g. Virial theorem 2 M V R G ) fail to be valid at non-Euclidean spacetime. Gravity introduces nothing locally. All the effects of gravity are felt over extended regions of spacetime. Gravity is geometry. The first natural step is to modify the underlie geometry itself. We modify the equation of motion in the updated hyperbolic geometry 2 r V e r a m mm    that fits the data and predicts the observed flat rotation curve without invoking Dark Matter. The lensing could be interpreted as a curved spacetime. The missing mass required to account for the observed lens is the same as the missing mass required to account for the observed flat rotation curve. We show that our hyperbolic equation of motion predicts the kinematics of the UDGs and traces their speed rotation curves. The hyperbolic spacetime curvature-not Dark Matter-accounts for such a missing mass. CMB physics-and consequently its presumed Dark Matter as an initial condition-is in trouble after the tension in the value of Hubble constant. Thus, the hyperbolic structure of the spacetime, not dark matter, accounts for the current anomalies in the observations.
Article
Full-text available
Cosmological models in which dark matter consists of cold elementary particles predict that the dark halo population should extend to masses many orders of magnitude below those at which galaxies can form1–3. Here we report a cosmological simulation of the formation of present-day haloes over the full range of observed halo masses (20 orders of magnitude) when dark matter is assumed to be in the form of weakly interacting massive particles of mass approximately 100 gigaelectronvolts. The simulation has a full dynamic range of 30 orders of magnitude in mass and resolves the internal structure of hundreds of Earth-mass haloes in as much detail as it does for hundreds of rich galaxy clusters. We find that halo density profiles are universal over the entire mass range and are well described by simple two-parameter fitting formulae4,5. Halo mass and concentration are tightly related in a way that depends on cosmology and on the nature of the dark matter. For a fixed mass, the concentration is independent of the local environment for haloes less massive than those of typical galaxies. Haloes over the mass range of 10⁻³ to 10¹¹ solar masses contribute about equally (per logarithmic interval) to the luminosity produced by dark matter annihilation, which we find to be smaller than all previous estimates by factors ranging up to one thousand³.
Article
Full-text available
The extended excess toward the Galactic Center (GC) in gamma rays inferred from Fermi-LAT observations has been interpreted as being due to dark matter (DM) annihilation. Here, we perform new likelihood analyses of the GC and show that, when including templates for the stellar galactic and nuclear bulges, the GC shows no significant detection of a DM annihilation template, even after generous variations in the Galactic diffuse emission models and a wide range of DM halo profiles. We include Galactic diffuse emission models with combinations of three-dimensional inverse Compton maps, variations of interstellar gas maps, and a central source of electrons. For the DM profile, we include both spherical and ellipsoidal DM morphologies and a range of radial profiles from steep cusps to kiloparsec-sized cores, motivated in part by hydrodynamical simulations. Our derived upper limits on the dark matter annihilation flux place strong constraints on DM properties. In the case of the pure b-quark annihilation channel, our limits on the annihilation cross section are more stringent than those from the Milky Way dwarfs up to DM masses of approximately TeV and rule out the thermal relic cross section up to approximately 300 GeV. Better understanding of the DM profile, as well as the Fermi-LAT data at its highest energies, would further improve the sensitivity to DM properties.
Article
Full-text available
We report the first dark matter search results from XENON1T, a ∼2000−kg-target-mass dual-phase (liquid-gas) xenon time projection chamber in operation at the Laboratori Nazionali del Gran Sasso in Italy and the first ton-scale detector of this kind. The blinded search used 34.2 live days of data acquired between November 2016 and January 2017. Inside the (1042±12)−kg fiducial mass and in the [5,40] keVnr energy range of interest for weakly interacting massive particle (WIMP) dark matter searches, the electronic recoil background was (1.93±0.25)×10−4 events/(kg×day×keVee), the lowest ever achieved in such a dark matter detector. A profile likelihood analysis shows that the data are consistent with the background-only hypothesis. We derive the most stringent exclusion limits on the spin-independent WIMP-nucleon interaction cross section for WIMP masses above 10 GeV/c2, with a minimum of 7.7×10−47 cm2 for 35−GeV/c2 WIMPs at 90% C.L.
Article
Full-text available
On 2017 August 17, the gravitational-wave event GW170817 was observed by the Advanced LIGO and Virgo detectors, and the gamma-ray burst (GRB) GRB 170817A was observed independently by the Fermi Gamma-ray Burst Monitor, and the Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory. The probability of the near-simultaneous temporal and spatial observation of GRB 170817A and GW170817 occurring by chance is . We therefore confirm binary neutron star mergers as a progenitor of short GRBs. The association of GW170817 and GRB 170817A provides new insight into fundamental physics and the origin of short GRBs. We use the observed time delay of between GRB 170817A and GW170817 to: (i) constrain the difference between the speed of gravity and the speed of light to be between and times the speed of light, (ii) place new bounds on the violation of Lorentz invariance, (iii) present a new test of the equivalence principle by constraining the Shapiro delay between gravitational and electromagnetic radiation. We also use the time delay to constrain the size and bulk Lorentz factor of the region emitting the gamma-rays. GRB 170817A is the closest short GRB with a known distance, but is between 2 and 6 orders of magnitude less energetic than other bursts with measured redshift. A new generation of gamma-ray detectors, and subthreshold searches in existing detectors, will be essential to detect similar short bursts at greater distances. Finally, we predict a joint detection rate for the Fermi Gamma-ray Burst Monitor and the Advanced LIGO and Virgo detectors of 0.1–1.4 per year during the 2018–2019 observing run and 0.3–1.7 per year at design sensitivity.
Article
Cold dark matter (CDM) constitutes most of the matter in the Universe. The interplay between dark and luminous matter in dense cosmic environments, such as galaxy clusters, is studied theoretically using cosmological simulations. Observations of gravitational lensing are used to characterize the properties of substructures-the small-scale distribution of dark matter-in clusters. We derive a metric, the probability of strong lensing events produced by dark-matter substructure, and compute it for 11 galaxy clusters. The observed cluster substructures are more efficient lenses than predicted by CDM simulations, by more than an order of magnitude. We suggest that systematic issues with simulations or incorrect assumptions about the properties of dark matter could explain our results.
Article
Dwarf galaxies move in unexpected ways Massive galaxies like our Milky Way are orbited by satellite dwarf galaxies. Standard cosmological simulations of galaxy formation predict that these satellites should move randomly around their host. Müller et al. examined the satellites of the nearby elliptical galaxy Centaurus A (see the Perspective by Boylan-Kolchin). They found that the satellites are distributed in a planar arrangement, and the members of the plane are orbiting in a coherent direction. This is inconsistent with more than 99% of comparable galaxies in simulations. Centaurus A, the Milky Way, and Andromeda all have highly statistically unlikely satellite systems. This observational evidence suggests that something is wrong with standard cosmological simulations. Science , this issue p. 534 ; see also p. 520
Article
For Newtonian dynamics to hold over galactic scales, large amounts of dark matter (DM) are required which would dominate cosmic structures. Accounting for the strong observational evidence that the universe is accelerating requires the presence of an unknown dark energy (DE) component constituting about 70% of the matter. Several ingenious ongoing experiments to detect the DM particles have so far led to negative results. Moreover, the comparable proportions of the DM and DE at the present epoch appear unnatural and not predicted by any theory. For these reasons, alternative ideas like MOND and modification of gravity or general relativity over cosmic scales have been proposed. It is shown in this paper that these alternate ideas may not be easily distinguishable from the usual DM or DE hypotheses. Specific examples are given to illustrate this point that the modified theories are special cases of a generalized DM paradigm.