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Could anyone define and explain the concept 'virtual' in Quantum Physics, Cosmology, Metaphysics, and Artificial Intelligence? Or, do such definitions exist?
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At least in the AI and internet worlds there is the discussion of virtual reality, virtual world, etc. Are these virtuals existent or just without existence? If existent, how and why? If not existent, how to clarify them in terms of the existent world?
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Would any such transition have occurred in increments locally, or all at once globally?
Is the idea of the transition from one era to the next designed to save an unlikely or incomplete theory?
Are there articles discussing these questions?
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RS:How does the universe know when to transition from radiation dominated ... to matter dominated ...
Robert Shour, the attached graph shows the energy density of the three components, the evolution of the scale factor depends on the combination of all three so there isn't a sharp transition but a smooth curve between them.
RL: The recent observation by the JWST of galaxies older than 13.79 billion years ...
Richard Lewis, that has not happened, galaxies have been seen at high redshift than previously but they are still about 170 million after the fiducial start, so about 13.62 billion years ago. They are very small as predicted, the surprise is that some are less unstructured than anticipated. There will be galaxies found even earlier than these but probably not before 13.76 billion years ago.
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Do such measurements make sense? Do they exist?
Comparing redshift and luminosity distances, if that is a sensible question, may bear on the 4/3 scaling hypothesis as it relates to dark energy.
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Cepheid and RR Lyrae variables are well known standard candles, and important tools in the cosmological distance ladder. For example, Cepheid variables, which were discovered by Henrietta Swan Leavitt, have the property that their luminosities can be directly inferred by observing their pulsation period, which then allows one to calculate their luminosity distance, given that the observing instrument (telescope) also measures their flux.
However, although nothing stops you from making redshift measurements of relatively nearby objects, this will induce an error in any cosmological parameters inferred from these measurements (such as the luminosity distance), because the peculiar velocities of these objects would be comparable to their Hubble flow, giving you highly inconsistent results. Luminosity distances calculated by interpreting the measured redshifts as cosmological redshifts, become more reliable at larger distances, where the Hubble flow dominates over the peculiar velocities.
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From the 1998 book Seeing Red by Halton Arp, at page 274.
Is that consistent with nullius in verba?
Do you agree with Halton Arp?
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Yes, it is natural to have suspicion and good to save careless steps.
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Cosmological explanations for our apparently fine-tuned universe are basically divided between a) a vastly huge multiverse of universes with varying fundamental force and mass constants, including the cosmological constant (where our apparently fine-tuned universe is just one universe in this multiverse), or b) a cosmic intelligence that fine-tuned our universe at its beginning to evolve stable galaxies, life and developed minds. In scientific terms, which explanation is preferable? Are there other options? Is a cosmic mind a viable scientific hypothesis for explaining our universe's origin?
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Dear Dr Richard Gauthier . I agree with Dr Joseph Badir ,
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Should the scholars at RG and elsewhere be alarmed by the press reports on the influence of the unholy alliance of big money and theology on high-value scientific research, particularly on theoretical physics and cosmology?
The British newspaper, The Guardian report: The MIT-Epstein debacle shows ‘the prostitution of intellectual activity’. https://www.theguardian.com/commentisfree/2019/sep/07/jeffrey-epstein-mit-funding-tech-intellectuals
BBC reports:
Big Bang and religion mixed in Cern debate
Big Bang: Is there room for God?
More on how Big Money, Beauties, "Big Minds" and Big Science converge:
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Dear Professor Abdul Malek
After a careful search in my records of research related to the Big Bang Cosmology I have realized that all interactions between big money, science and religion mentioned in your question are much more complicated that it is openly admitted. Please consider the following quote describing the seminal contribution of a Belgian scientist who should be credited as a sole creator the Big Bang Theory:
”…Appealing to the new quantum theory of matter, Lemaître argued that the physical universe was initially a single particle—the “primeval atom” as he called it—which disintegrated in an explosion, giving rise to space and time and the expansion of the universe that continues to this day. This idea marked the birth of what we now know as Big Bang cosmology.
It is tempting to think that Lemaître’s deeply-held religious beliefs might have led him to the notion of a beginning of time. After all, the Judeo-Christian tradition had propagated a similar idea for millennia. Yet Lemaître clearly insisted that there was neither a connection nor a conflict between his religion and his science. Rather he kept them entirely separate, treating them as different, parallel interpretations of the world, both of which he believed with personal conviction. Indeed, when Pope Pius XII referred to the new theory of the origin of the universe as a scientific validation of the Catholic faith, Lemaître was rather alarmed. Delicately, for that was his way, he tried to separate the two:
“As far as I can see, such a theory remains entirely outside any metaphysical or religious question. It leaves the materialist free to deny any transcendental Being… For the believer, it removes any attempt at familiarity with God… It is consonant with Isaiah speaking of the hidden God, hidden even in the beginning of the universe.” “
Source:
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The foundation of physically reality is necessarily very simple and quite probably its structure cannot observed. But recently I came to the conclusion that the signature of this foundation can be observed in all aspects of the universe. All separated items in universe are either modules or modular systems.
Is modular configuration a fundamental characteristic of physical reality?
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Reflect: what came first, consciousness or the brain? If consciousness, then the brain has been created in consciousness. If the brain? No that is ridiculous!
Primitive humans surely had no idea of the brain, (except to eat it!) but they were just as surely conscious.
The concept of the brain (and all other things) has accumulated through experience, shared by communication, as a phenomenon we now share as "reality."
Today, to understand reality in any other way is simply an attempt to pose one reality as superior (more real) than others. This is a game that has played out historically as a function of force or fraud, i.e., a function of power.
If we want reality to be any more than the result of power play, we must understand it as a phenomenon within consciousness. And deal with that reality!
Respectfully,
Kurt
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Cosmology is difficult because space, time and the sizes of cosmological things are at scales vastly larger and smaller than are easily perceived by human beings. To guess what the universe is like requires extrapolations. But extrapolations are based on the assumption that what we can witness, see and measure corresponds to what we can’t witness, can’t see and can’t measure. Is cosmology science? Is it a science-in-waiting? Does cosmology become science when its ideas are confirmed by astronomy?
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Yes. Learning about the formation and development of other constellations, planetary systems, other exoplanets on which life may exist allows you to expand the resources of knowledge about the formation of the planet Earth and the origin of life on our planet. It is pure science.
Thank you, Greetings,
Dariusz Prokopowicz
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It is commonly accepted that General Relativity has its own 'bare' cosmological constant that contributes together with the cosmological constant resulting from vacuum energy density for an effective cosmological constant. Are there any candidates for this 'bare' cosmological constant?
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Dear Stefan Ruster,
"quantum theory is correct."
Quantum theory in general is no more than a bad joke. Every one of these so-called theories is almost completely wrong. Quantum Mechanics, on the other hand, Is the best mathematical system that we have to make predictions in the quantum world. But the logic of it is no better than 'woo' physics.
Advocates of the logic and theories believe that local hidden variables have been dis-proved, but they are wrong. Einstein believed there was no such thing as an aether based upon his proposal of Special Relativity. For this reason, he proposed warped space in General Relativity. But he too was wrong for the same reason.
Since Einstein's proposals we have observed the Zero-Point-Field for more than 70 years now. We have proposed the Higgs field, dark matter, dark energy, gravitons, quantum foam etc. Even if some of these fields are pure fantasy, there are proven background fields that could rightfully be called an aether.
For the theory of quantum mechanics to be correct none of these fields could be involved with the quantum world. For General Relativity to be correct, none of these fields could be involved with gravity. Since both of these theories require the non-existence of these fields at solar-system scales they can be mathematically correct, but both theoretically wrong for the same reason. That's why IMO they don't and cannot agree with each other, and why no theory of everything could ever be correct without the inclusion of at least one background field that interacts at all scales to explain reality, mathematics aside.
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According to Weyl and Chandrasekhar, general relativity (GR) is a triumph of speculative thought. But it is a well-known fact that GR is initiated by two analogies. Analogy is known to be a weak reasoning in science and philosophy. To redress the case this type of reasoning is renamed as Equivalence Principle (EP) in relativistic physics. The renaming, however, could not hide the fact that the presented analogy was not flawless. Irrefutable disproves were side-stepped and the analogy was instated to be the seed of new kind of physics. EP was defended by reducing the size of the lab and the duration of the experiment. This type of defending is like the proponents of flat-earth idea defend their case by reducing the patch of the land for examination until their pseudo-science theory is proven.
The attached document is a short description of EP analogies and its well-known critics. The document also introduces a new EP based on Uniform Deceleration of a spaceship in open space. This new analogy results in a different curvature of light in comparison to what original EP has established using uniform acceleration. The author believes that none of the conclusions from EPs should be allowed in science as they are based on inconclusive comparison/analogy and they ignore glaring flaws in the argument.
The author would like to present this new EP for discussion and criticism.
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I agree with all your criticism.
JES
p.s.
It would be interesting to see a new theory evolve from your insight.
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Should a manned mission to Mars, which could be implemented in a few years, be an international mission, or rather a national one, inspired and organized according to the familiar concept of the 1970s, of international rivalry of the leading economically and politically largest countries?
Apparently a manned mission to the planet Mars is now technically possible.
Researchers working on space exploration programs argue that it is technically possible that humans already have the necessary technology to carry out a two-year manned mission to Mars.
First of all, it is necessary for the US President to issue a program of a manned mission to Mars.
A similar program in the 1980s was announced by then US President John F. Kennedy.
The plan of a manned mission to the moon was fully realized at that time.
However, the current mission to Mars, technically possible, would require large financial outlays for the implementation of this mission.
Perhaps it would be necessary to organize an international consortium that would organize an international manned mission to Mars.
Maybe it could also be an international crew of this mission?
Then mission costs could be spread over several countries and it would have global significance in terms of international cooperation.
The previous analogous manned space mission, i.e. the manned expedition to Earthly Princes in the 1970s, had the significance of political rivalry between the then US and the Soviet Union.
It was a symbolic technological race.
Is the planned manned mission to Mars also inspired by this type of international competition, for example between the US and China or possibly also some other countries?
China is rapidly developing technologically, aspiring to become a global powerhouse in a few years time. 1 not only in the scope of production of various goods and economic growth but also in the matter of having the most modern innovative technologies implemented in various economic applications.
In the US, a very large, historically high public debt can be a significant finns barrier to finance and thus the USA will organize a manned mission to Mars in the next few years.
If this mission to Mars is mainly inspired by this new international rivalry in terms of having technological capabilities, it is currently difficult to predict which country will win the race and be the first to organize manned missions to Mars?
In view of the above, I ask you with the following question: Should a manned mission to Mars, which could be implemented in a few years be an international mission, or rather a national one, inspired and organized according to the familiar concept of the 1970s, of international rivalry leading economically and politically the largest countries?
Please reply. I invite you to the discussion
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Same as fighting the COVID pandemic, we have the technology and know-how ... but not the wisdom to work collaboratively. #Greed #Ego #Individualism
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(using simple  example or logic)
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@Sergey Shevchenko
"- what is  space, time, and spacetime? – the space and time as possibilities for anything to be existent form the spacetime, which is, first of all, nothing more then some “empty container”, where the system “Matter” is placed;"
Is it really an "empty container" that matter is place in as it seems that you are making a rather large ontological jump in assuming a long held dichotomy of spacetime and matter.
"- what is notion “absolute” relating to the space [time and spacetime]? The “absolute” space/time/spacetime in this case means that this spacetime doesn’t depend on – what is placed in it; including masses, reference frames, etc. And that is indeed so."
That's is one way of approaching it but even people holding on realist interpretation of General Relativity could see such a spacetime as an absolute background in the sense that it exists (separate or emergent from matter). A better word would be immutable (matter does not determine its structure/curvature though it could be curved regardless) while absolute i'd reserve for having certain features associated with Newtonian spacetime including an abundance of absolute quantities which with respect to the absolute spacetime background (absolute velocity or the correct ticking of the universal clock) are empirically inaccessible.
"I.e., simply in the  reality there is/are no “non-absolute” space/time/spacetime, including so called “relativistic effects” (“dilation”, “contraction”, “curvature”, etc.) that are postulated in the special and general relativity – they simply don’t exist. That’s all."
'Simply don't exist', what's wrong with objects contracting in length because of inherent dynamical features in our physical laws or having a back ground spacetime imbue these frame dependent features.
"There can be no proof that space is not absolute, because there exists a viable theory of gravity where space is absolute, and what looks like curvature is simply caused by distortion of clocks and rulers by the ether.  An ether theory, yes,"
Please do not confuse the dynamics of a persistent all present ether and the inherent local or global spacetime structures/symmetries. You can have a spacetime which gives rise to the dynamical features we observe (Lorentz invariance or our field laws) or we could assume some background Galilean spacetime with already inherent dynamical features of our field laws. The chicken or the egg but in most situations it will turn out to be, in my opinion, empirically indistinguishable.
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Suppose there is a static 3 dim space and a dynamic changing 4 dim space. Without that supposition, lots of problems in physics remain puzzles. With it, lots of puzzles are easily resolved.
Energy in 4 dimensional space, where the fourth dim is proportional to the distance light travels or the time it takes for light to travel that distance, has 4/3 as much energy per dimension as does 3 dim static space. Hence, dim space a 4/3 length L when 4 dim space has a distance of length L. This appears to account for space expanding. A supernova’s distance from Earth measured in the 4 dim space where light moves, using redshift, should appear to be 3/4 as luminous when comparing type 1A supernovas, because in static 3 dim space the supernova is 4/3 as far. Other data is consistent. Energy density for dark energy (so called) compared to matter energy density is in the ratio [ E/ L^3] : [ E/ {(4/3)L}^3, which is 4^3/3^3 which is about 0.7033/ 0.2967, as has been observed in astronomy.
There are numerous examples of this 4:3 ratio occurring a variety of different natural phenomena, as set out in various article in my projects dealing with the 4/3 laws and DE.
Or maybe not?
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The history of science shows that the universe does include two reference frames, (1) one static three-dimensional space and (2) the other dynamic containing four-dimensional space. The classic mechanical physics of Isaac Newton's three Laws of Motion is a locus classicus for (1), and Albert Einstein's discovery of the photoelectric effect exemplifies a dynamic inroad in our understanding of the physical laws of our cosmos. Thus, the mathematically formulated proof for (1) F = MA; and for (2) e = mc2 will have to be followed by yet a third (3) discovery of (A) a formula, with (B) mathematical proof, of the next step, if any, that improves on the revolutionary advances made by the scientific community that culminated in the breakthrough discoveries of Newton & Einstein.
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It has radically altered it by rehabilitating Fritz Zwicky 1929.
Hence ten Nobel medals are gone. And cheap energy for all is made possible. Provided, that is, that humankind is capable of mentally following in Yakov Sinai’s chaotic footsteps. If not, energy remains expensive and CERN remains dangerous to all: A funny time that we are living in. With the crown of Corona yet waiting to be delivered.
April 1st, 2020
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Please, elaborate.
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Dear Colleagues,
I am a liaison (informal) at my university between science and the arts. I have family in planetary astronomy but this is far afield.
A question or two:
What does this newly-reported Radcliffe Wave of gaseous proto-stars tell us about how our galaxy originated?
Is there any chance that this wave will make some difference in our own sun's behavior?
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Dear Preston,
Intriguin view, thanks for sharing Vera Lima
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I want some help in being able to clearly perceive the expansion of the universe and the consequences thereof.
We know that the universe is expanding in an accelerated manner. It is my understanding that space alone cannot expand without affecting the local time. Thus as per GTR, depending on the curvature of space-time and the energy density, time too shall suffer a change due to the changing space.
Assuming that there is no curvature of space-time and no mass or energy contained in a chunk of space (assuming the zero-point energy of empty space as zero) between two galaxies A and B, let us say that the local time at a point P in this space goes as t0. If we on Earth could somehow observe this point and measure the time at P as t,
  1. When we talk about the rate of expansion for example as in Hubble's Law, do we follow the comoving coordinates or the proper coordinates?
  2. How would t and t0 relate to each other if the rate of expansion is uniform and accelerating respectively?
  3. How much is 1s for the comoving observer at the inflation period in terms of the usual 1s now on Earth?
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Dear Bibhusit Tripathy,
Thank you for the interesting question. As I visualize it: In the comoving coordinates of the Friedman-Robertson-Walker (FRW) metric, g00=1 and so time is not dilated between galaxies, but is universal throughout all space, where space is defined as that three-dimensional slice of FRW space-time such that dt=0. A clock between galaxies comoving with the galaxies would thus not show time dilation in FRW coordinates. This is true regardless of whether the scale factor a(t) is accelerating, decelerating, or increasing linearly with time. However, if we use coordinates in which galaxies recede at a certain velocity (which I believe you call "proper" coordinates), then a clock between two galaxies moving with the galaxies would show time dilation as given by special relativity. This is not a paradox. In FRW coordinates, space is a different slice of space-time than it is for "proper" coordinates. Essentially FRW space, or the t=constant slice of FRW space-time, extends further and further into the future as r increases, as compared to space in "proper" coordinates. Regarding question 1, the Hubble expansion in FRW coordinates refers to the expansion of space itself, while in "proper" coordinates, it would be interpreted as due to the motion of galaxies. I am currently working on this problem and may write a paper on it.
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This question requires explanation. Discussion on the second day of Galileo’s Two Chief World Systems raises the point.
Simplicio, taking the position of those opposed to Copernicus, doubts the Earth moves; if Earth moved it would have to move at too great a speed. Sagredo and Salviati say this objection has no merit. The fixed stars have a radius far greater than the Earth, and yet the implied speed, much greater than that of the Earth in the Copernican conceptual reference frame, does not undermine the belief of the anti-Copernicans in their objection. Here is an inconsistency.
The inconsistency is not encountered in modern times that takes for granted the heliocentric model of the solar system. This argument, based on the large radius of the distant stars, is one not usually encountered. One supposes that is so, because it is unnecessary. But then the question arises. Does society lose or forget these old insights that are discarded once new conceptual reference frames take hold? Or, perhaps, is nothing lost?
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Hello @Robert Shour,
On the question, "Does society lose or forget these old insights that are discarded once new conceptual reference frames take hold?" Yes, in the sense that too much "knowledge" eclipses common sense. A case in point is what I call the "Wimbledon Phenomenon". A couple years ago, British social scientists conducted a survey among 1) Housewives, and 2) Tennis trainers, asking who would win the next Wimbledon championship. The housewives out-performed the tennis trainers by a large margin.
It could also be argued that the Friedman-Robertson-Walker metric (as "a new conceptual reference frame") and its attendant big bang theory and LambdaCDM cosmological model have eclipsed all common sense about the nature of the universe, insofar as huge contradictions now exist in standard cosmology, for example related to Dark Energy, which has a phantom equation of state p<-rho and therefore behaves like anti-gravity. Yet this does not undermine the Mainstream Physicist's continuing belief in their objections to refutations of LambdaCDM!
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Dear all,
in accordance with Friedmann-Lemaitre-Equation there are three different possibilities of space curvature which can be described mathematically and imparted graphically or analogously (Closed, Openend or Flat Universe). In the attached poster a fourth graphic representation is shown, which is however only graphically derived.
Is this sketch describable within Friedmann-Lemaitre-Equations? How can we interpret this sketch? A Universe that is truly infinite, although it has a defined start and a defined end point?
What would be a 3-Dimensional mathematical object to describe the plot (closed hypertorus, while closed means without a connection in the center?). And what numbers for curvature parameter k and density Parameter Ω make sense for this sketch?
I have created this plot purely graphically and wonder whether a mathematical interpretation of such a shaped space-time is possible, or whether it inevitably leads to paradoxes and is thus a graphic that can be drawn abstractly, but ultimately makes no mathematical sense.
Thank you!
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I might add that my paper on a "Bipolar Model"...of hyperbolic space was rejected by Physics journals as being too mathematical and by Mathematics journals as being too physical. It primarily raises the question of what coordinates are "physical". This is not easy to answer. For example rotating coordinates are considered non-physical, but if you are in them, they are real and there is physics associated with them. As mentioned above, one needs to consider the matter distribution to make sense of them.
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Dimension is fundamental. Was it present at creation of the universe? Did it play a role in creation of the universe?
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Dear Robert Shour, the dimension of the Universe and cosmogenesis, respectively, is determined completely by human perception for given stage of human evolution. We consider the space where we live as 3-dimensional one. Einstein created the theory where the time is the 4-th coordinate of the curved space-time. Contemporary scientists assume that the time flows only from the past to the future. Of course, General Relativity creates more bread picture of the World. But it is evidently that the model of the World will be more complete in further. Contemporary scientists study 4-dimensional models of the Universe. Why must we consider only 4 dimensions? Why the time must possess only one dimension and why it must flow only from the future. Our models of the Universe correspond to our consciousness at the given time. When human consciousness reaches more high level, people will consider our people as multidimensional one.
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I have found two different results for the effect of dark matter on the orbital speed of the Sun. One from Wikipedia suggests there is no effect while another one from astronomynotes suggests there is a substantial effect. Which one is correct? Both Figures and their captions are attached.
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Dark matter density is 6x10-22 KG/m3, radius of earth's orbit 1011 m, therefore amount of dark matter within earths radius is, (4/3) x π x 1033 x 6 x 10-22=2.53 x 1012 kg. This is much smaller than the mass of the sun which is 2 x 1030 kg. Thus we cannot feel the effect of dark matter compared to sun's gravitational pull.
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The universe as a whole is much larger than the portion we can measure. That "observable universe" (OU) has a proper radius of around 43 billion light years. The Planck mission measured the curvature density ΩK of the OU as 0.0±0.005. For the positive 1 sigma value, that suggests the whole would be a 3-sphere with a radius of ~210 billion light years but inflation suggests the curvature should be much closer to zero, hence the whole would be far larger, probably many orders of magnitude. For zero or negative curvature, the spatial extent would be infinite.
If we assume that the whole is much larger than the observable portion, we could think of many alien species scattered throughout the universe but so widely separated that there is no overlap between their respective OUs. While the universe would have a mean curvature density, there are also statistical variations, so we can think of producing a histogram of the values of ΩK for all these uncorrelated regions, each around 43 billion light years in radius.
The Harrison-Zel'dovich spectrum tells us the two-point correlation of density as a function of separation of sample points. Specifically, it would be a power law with slope 1 but quantum effects predict a slightly smaller value and it has a measured slope of 0.96 (Planck mission results, 2015). The same results also gave a null result for "running" of the spectrum, which means it appears to be linear, no quadratic term, and there is no evidence of non-Gaussianity, which means the distribution can be assumed to be the standard bell curve.
My question is: what would be the standard deviation of the samples of ΩK measured over a large number of non-overlapping regions, each the size of our observable universe?
If anyone needs more background, I can provide links to introductory articles and some undergraduate lectures. This is the relevant section in the Planck results paper:
P.S. If you don't accept the standard model of cosmology or have your own alternative, don't waste your time replying, I am looking for a purely mathematical answer based on the conventional model.
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Dear George,
Back to my first suggestion, please try using my method, which I have created the calculator, i.e. http://sigitharyadi.net/multidicipline/non-intercept-linear-regression-id/Procedure: (1) From the data you have, specify the dependent and independent variables, where you are sure that there is a linear relationship that does not have an intercept (i.e. when the independent variable is 0, the independent variable must be zero), (2) Use my website, then you will get a regression equation accompanied by the level of correlation between two variables you have set, and the confidence level of the regression equation, (3) After that, you can use the regression equation to extrapolate to the area outside the range of your measurement data (and possibly for an interpolation within the measurement area), where the standard deviation or variance, or the possibility of miscalculation is equal to one minus the correlation index of the calculation you get from the my calculator.
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Geodesics in a curved finite space are not parallel. Volumes transported over cosmic distances therefore will alter their shape and orientation in respect to initial conditions.  If compared with the initial condition, the volume length in direction towards a receiver becomes increased during the transport; the receiver of radiation out of that volume will notice a red shift and a time dilatation. His immediate impression will be that an according expansion of the universe must have occurred. But it was only a curved space effect, which has caused a modification in shape, extension and orientation of the volume filled with radiation.
Could this answer some of the unsolved problems in cosmology?
C.f. Wikipedia; List of unsolved problems in physics; Cosmology and general relativity
Cosmic inflation
there is no cosmic inflation, the geometry of the universe is static.
Horizon problem
there is no horizon problem. The universe is closed. If we continuously go in any direction we finally will arrive at the starting point.
Origin and future of the universe
there is no origin, the universe is and stays eternal.
Size of the universe
the size is finite and can be determined from the length dilation on volume transport and the according red shift numbers.
Baryon asymmetry
the universe always had been filled with baryonic matter. Black holes are involved in coordinated recycling processes.
Dark anything
gravitational influence must be recalculated based on the static, finite, isotropic and homogenous geometry. In analogy to geometric influence on transported light, an influence on transported matter may exist. The deformed view on the transported images of galaxies also requires recalculations.
Axis of evil/Copernican Principle
the problem does not exist because the microwave background looks about the same in any direction at any place in the universe.
Shape of the universe
mathematically the shape of the universe can be described by a mapping of finite Cartesian coordinates to unit quaternions. A displacement corresponds to a multiplication with the according quaternion. This means that any displacement only alters the direction of the three dimensional view on the universe.
Could this model answer further questions or do more severe unanswered questions arise?
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Wolfgang, answer to your questions are in the paper "Illusion of space expansion ....." on this site. and other papers by us. Take a look 
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Or general steps controlling the "birth" and "death" of a sinkhole conceptually similar to Wilson's cycle in plate tectonics?
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I'm not aware of a formalised theory/framework of this.
It's going to depend on the type of sinkhole as well. For a suffusion sinkhole (for example) then it is more progressive, rather than having a fixed end point, so it's hard to conceptualise a "death". Whereas for a cover collapse type sinkhole in karst terrain, then it could be conceptualised as the start of the dissolution of limestone is the "birth" of the sinkhole or the start of the overall process. Then once the void is sufficiently large to create a void into which the caprock collapses this is the "death", as it is the end of the active process. It tends to be the case that caprock type sinkholes aren't progressive. That is to say, once the true sinkhole has formed the feature is no longer "active" and it is rare for them to keep expanding.
There certainly isn't a conceptual theory of this though, in text books for example. It's an interesting angle to ponder.
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Full disclosure: I'm a protein biochemist and a cell biologist. I have no expertize in physics or cosmology.
But I have been mesmerized by documentaries on black holes on science cable channels.
One of many things that I do not understand is the different depiction of massive and super massive black holes.
Since their mass has collapsed into a single point, shouldn't all black holes be the same size in 2D, regardless of their mass?
Why are black holes depicted as a big black planet-like objects with swirling gas around them? 
Is it more appropriate to depict them as a drain (like a flushing toilet)?
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Schwarzschild radius of the neutron star is much smaller than the radius of the star therefore it cannot arrest the light emitted by its surface. When proton and electron combine they do not annihilate each other but proton gets transformed into neutron.
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Dark energy has a finite density, approximately 68% of the total energy density of the Universe. Assuming for simplicity a nonvarying Hubble constant H, our cosmological event horizon is at a distance c/H away (c = speed of light). Since c/H is finite, the total dark energy within our observable universe is finite. If the actual Universe is infinite, extending forever beyond our cosmological event horizon, then the total dark energy is infinite, but that beyond our cosmological event horizon can never interact with us. But the above neglects the negative gravitational potential energy of the dark energy in the gravitational field of the Universe. Counting this negative gravitational potential energy, the total energy of the Universe is zero.
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This is a rebuttal to a reviewer's comment about my claim that Absolute Peak Luminosity of type 1A Supernova are proportional to G^(-3) rendering Apparent SN1a distances having a dependence to G^(3/2)
Let me know if you disagree that I kicked this objection to the curb and thus all Supernovae distances are overestimated by G^(3/2) !!!!!  :)
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REVIEWER:  I’m also skeptical that the luminosity of a SN Ia if G were different would scale as G^-3 (or M_ch^2).
Ni-56 production is not a simple rate-limited process; SNe Ia undergo a deflagration that (in most cases) transitions to a detonation. They burn about half their mass to Ni-56 (depending on when the detonation occurs). Even if Ni-56 production were a simple process, the radius (and thus the density) of the white dwarf also changes with G.
ANSWER: Firstly, let’s consider the reviewer's assertion that density in a White Dwarf also changes with G. That is incorrect. Detailed derivation was contained in appendix and is reproduced below.
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I corrected an assumption about Luminosity and Mass.  Now it is perfect...:)
This argument proves that Luminosity depends upon G^(-3) and since G is epoch dependent in my theory and proportional to the inverse of the 4D radius of the Universe, earlier epochs had stronger Gravitation. Stronger Gravitation means weaker SN1a, resulting in overestimation of distances.  The farther the SN1a is, the larger the overestimation.
The distances are overestimated by G^(1.5).  Once one corrects them, Inflation Theory disappears in a puff... The same goes to General Relativity and Dark Energy....:)
The argument supporting this dependence is based on the work of David Arnett about type II Supernova Luminosity. This is an estimation of the dependence of the Luminosity with G.
To extract the dependence, we force the radius of the Supernova to have a Chandrasekhar radius dependence. We also estimated the M0 (Sun mass) dependence upon G. The Sun mass is a relative mass reference within the context of Supernova mass. Supernovae occurs in the dominant radiative pressure (as opposed to gas pressure) regimen.  Under that circumstance, the Luminosity dependence comes up as Luminosity Proportional to G^(-3).
Needless to say, this derivation is trivial and consistent with Supernovae and Star models.
It takes just one page to be derived, easy as Butter.  (of course, after David Arnett did all the hard work...:)
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This means that the SN1a ruler, which is the basis of Cosmology and Astrophysics would be faulty under an epoch dependent G context.  Since HU is epoch-dependent and predicts the Supernovae distances perfectly and without any parametrization, that places the Standard Model in a very precarious position.
If you add to that, HU observation of Neutronium Acoustic Oscillations or NAO... (which is what Algebraists should be saying right now...:)  I think, there is reckoning coming...
See the NAO... SDSS had this data for 10 years. Since they are basically Algebraists and see the Universe according to GR, they cannot imagine acoustic waves along distances. The Universe is supposed to be Uniform...
HU sees oscillations primarily along distances (which corresponds to cosmological angles).  There may or may not be cross-talk with the 3D angular modes.   I say that because I don't see the 150 Mpc wavelength in HU 2-point correlation.
So, How Long will the Community refrain from welcoming my conclusion that there was no Big Bang (there was Many Bangs) and that the Universe didn't come out of a fiery explosion, dilation is nonsense, vacuum fluctuations driving a Big Bang are utterly nonsense.... GR is nonsense..etc.
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Below is the Hypergeometrical Universe Theory (HU) to the question of how environments with different Gravitation would affect the Absolute Luminosity of SN1A Supernovae.
The derivation starts with the work of David Arnett on type II Supernova.  We apply type 1A Chandrasekhar radius G dependence to the thermal Energy and to R0. We also scale a Sun Mass by modeling the Sun mass under different regimen - Low and HIgh radiative pressure.
This is an estimation to see if they expected dependence is consistent with astronomical observations, so the precise value is less relevant than the range.
Astronomical observations are consistent, within the logical framework of the Hypergeometrical Universe, with a G^(-3) dependence. That is exactly what one obtains using the High Radiative Regimen to evaluate the mass of the Sun G dependence.
That said, irrespective to which model we useed the range varied Between G^(-3.5) and G^(-3).
The relevance of this results is that in HU, G is inversely proportional to the 4D radius of the Universe. 
The Standard Cosmological Model considers that the Absolute Luminosity of a SN1a is constant or standardizable (variations due to different amount of ejecta are renormalizable through the empirical methodology WLR).
HU proposes the G is epoch-dependent, which would make SN1a to be epoch-dependent in a way that farther away SN1a had intrinsically weaker explosions and thus reduced Luminosity. Our adjustment of David Arnett's work indicated a G^(-3) Luminosity dependence.
That would result in an overstimation of the distances of Supernovae by G^(1.5).  After correction of the distances we can compare HU d(z) predictions with the astronomical observations.  See plot below:
The results below are consistent with 
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how can I find observational data for circular velocity of spiral galaxies (v(r)) versus the distance from the center of galaxies(r)?
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NASA starts Stealing my Gravitation theory:
“The majority of Ferent matter(Dark matter) is the core of the supermassive black hole” Adrian Ferent(Jan 14, 2015)
NASA --"Primordial Black Holes Formed in 1st Fraction of a Second of the Universe Could Function as Dark Matter" (The Weekend Feature)
October 29, 2016
“Black holes formed in the universe's first fraction of a second -- could work as dark matter." Kashlinsky said (May 24, 2016)
Ferent matter is Dark matter – Adrian Ferent (Jan 14, 2015)
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It is not known wether axions where formed before or after the inflationary epoch. It is usually assumed that axions are produced during inflation, during the GUT symmetry breaking phase which are energies of the order of the GeV’s scales (between 10^11-10^16GeV’s).

 Nevertheless, there are models which work on the production of axions just at the end of the Big Bang/before inflation, if this were the case the energy scales of axion production could even reach the TeV energy scale. Is this a correct claim?
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Ours business is to understand, or to try to understand, at least, what is happening in very straong gravitational, magnetic, electric fields... Or what is Physics near Black Holes, Neutron Stars, White Dwarfs, at very Great distances or redshifts.
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The symmetry between matter and antimatter is thought to have been broken in the early universe a short time after the end of cosmological inflation (« baryogenesis »). Matter and antimatter annihilated each other except a small excess of baryons and leptons which outnumbered their antiparticles and are at the origin of all the matter content of the universe. This is still at theoretical level (no experimental proof). However the pressure has probably changed very quickly from negative (inflation …) to positive (cloud of baryons and leptons). Also the energy produced by the annihilation must have gone somewhere. Could anybody give a simple digest of what physically occurred during baryogenesis and of the orders of magnitude according to the most accepted model(s) ?   
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Dear Esa,
Thank you for your answer with some hints on an alternative model you would like to go more thoroughly into. On this, I would just answer as Alexander Fleming, known to be extremely sparing of his words, did once after having listened to the tea-time discussions about several ongoing projects in the laboratory he worked in and having been requested for an advice. Question : “What do you think, Dr Fleming ?”. Answer : “Try”. So, just try, if nobody could sufficiently convince you to stop. You don’t know which new ideas will become the bases for breakthroughs within 50 or 100 years !
I must anyway say that I find several interesting ideas in the alternative models referred to in an amount of RG questions.  However, I feel very unfamiliar with them ! Even in front of the standard ΛCDM cosmological model which is the one I best understand, I feel poor : reason for the present RG question.  
I’d like to know as much as possible the ins and outs of what baryogenesis can tell us about the evolution of the universe in the framework of this model, before to decide to abandon it (or not) for an alternative model.
So, thanks a lot for your hints which open the mind (see also your answers to former questions) and apologies for not reacting in details at present time.   
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From the deceleration parameter q=−(a¨a/(a˙)2)   ---------(1)
where a is the scale factor.
Hubble's parameter H=a˙/a    ------------(2)
Substituting equation (2) in (1),
q=−(a¨/Ha˙) ---------------(3)
Making a¨ the subject in equation (3),
a¨= −(qHa˙)
This clearly shows that there is a link between the magnitude of the Hubble's constant and the acceleration value of the Observable Universe.
The present day value of q is approximately −0.55.
Is my proposal correct?
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Max, it would avoid a lot of confusion if you used the standard symbols for the parameters. The letter a is usually the scale factor, q is used for deceleration and c is the speed of light.
ME: Is the acceleration value of the expansion of the Observable Universe the product of Hubble's constant and the speed of light?
No, it is defined as the product of the scale factor and its second derivative divided by the square of the first derivative. See the first link.
ME: From Hubble's constant being equal to the second divided by the first derivative of the scale factor ...
No, the Hubble parameter is the first derivative divided by the scale factor, see the second link.
ME: C is the speed of the farthest galaxies in our Hubble volume which move at light speed.
All sources beyond roughly z=1.6 are receding at more than the speed of light. The farthest known galaxy is at z=11.09 and the CMBR comes from z=1089.
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May I have your opinion on the solution of Black Hole Information Paradox proposed in the attached  
TEDx talk?
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Andrew Worsley,
Looking through your An Advanced Dynamic Adaptation of Newtonian Equations of Gravity I find that it has a fundamental defect with respect to GTR: your equations have no time dependence. Thia means that you, just as Newton,, assume that gravitational effects propagate with infinite velocity. If Mercury would fall into the Sun, that would be felt immediately and withot time delay throughout the whole universe. The recent observation of gravitational waves is the experimental proof, that this is not so. Therefore I suggest that you correct your Advanced Dynamic Adaptation of Newtonian Equations of Gravity. to be more in agreement with GTR.
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In 1920 Eddington published a book Space, Time & Gravitation on general relativity which included an ingeniously simple derivation of light bending using general relativity.  The book may be found at a link below, and the explanation is on page 99.  Einstein used essentially the same explanation in The Meaning of Relativity published in 1922 (also linked below), in the vicinity of equation (107).  A coordinate transformation is made so that coordinate light speed is isotropic and Huygens bending, also known is the Fresnel principle, is applied.  The answer is taken at face value without re-transforming coordinates.
Using a graphical analysis of Huygens bending, I concluded that it is not coordinate independent.  See image attached.
Has there been any discussion of this method since 1922?  Is it still considered correct?
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There has been a comment recently in the Journal of Physical Mathematics about light bending in General Relativity.
It appears that when the internal structure of photons is clearly understood, there is no need to resort to GR spacetime curvature to explain the correct light bending angle.
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The big bang in classical general relativity involves a space-time singularity, a point of zero volume, infinite density, and infinite space-time curvature.  This involves the interesting topic of how to handle infinite values in physical theories as well as the limits of applicability of theories.
In most areas of physics the appearance of a singularity or an infinite value of an experimentally measurable physical quantity can be taken a a sign that we have reached the limits of applicability of the theory. One example is the ultraviolet catastrophe where applying equipartition of energy to the normal modes of the electromagnetic field emitted by a blackbody (a perfect absorber and emitter of radiation) in thermal equilibrium results in an infinite amount of energy at short wavelengths (so we should be blasted by an infinite amount of energy while sitting in front of our fireplace). This was solved by Planck with quantization of the emission and absorption of electromagnetic energy.
In some cases an infinite value is considered "benign" and removed by a procedure such as renormalization or regularization. The value of the "bare" charge of an electron in QED (quantum electrodynamics) is infinite but this is not the value which results from a laboratory measurement of the charge. This apparent infinity is removed by renormalization which takes virtual higher order effects into account to produce a finite value corresponding to what is actually measured.
General relativity has sometimes been described as the only area of physics that takes its singularities seriously or literally, whether it is the initial singularity at the big bang or the singularity at the center of a black hole.  There are even singularity theorems which specify the conditions under which singularities occur. This takes place in a classical space-time with no quantum gravitational effects. Once again the occurrence of a singularity is really a sign that our theory is breaking down and that a new theory, in this case a theory of quantum gravity, is required. It is generally believed that this occurs at a finite but very small scale which for distance is referred to as the Planck length, approximately 10^-33 cm, beyond which classical general relativity no longer applies (Technically it is the space time curvature which is important here. When the curvature is of the order of one over the square of the Planck length then quantum gravitation effects are expected to be important). This length scale is extremely small and is approximately 10^-20 times the diameter of a proton.
Thus while extrapolating backwards in standard cosmology appears to lead to a singularity of zero volume, infinite density and infinite space-time curvature, classical general relativity is no longer applicable at a stage before the singularity occurs when all relevant quantities are still finite. Until a full theory of quantum gravity is available we can only make limited and speculative statements about what may happen at smaller scales (greater space-time curvatures). 
As a final note, for completeness I should point out that there exist alternate theories of gravitation and alternate cosmologies that find various ways to get around this problem. Three examples are John Moffat's MOG or modified gravity, Roger Penrose's Conformal Cyclic Cosmology and QSSC or Quasi-Steady State Cosmology of Hoyle, Burbidge and Narlikar. In general there are far fewer people working on these theories compared to standard general relativity and cosmology and thus far fewer resulting publications. It should also be pointed out that these alternative theories are generally not accepted by the (vast) majority of relativists and cosmologists.
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  Hubble’s law doesn`t explain why distant objects were receding fastest. Conversely, a distant observer will see that the distant objects (those nearest to us) are receding fastest than those nearby (those distant to us).  What causes such illusion? 
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Charles, The peculiar local velocities  of galaxies in the group do not affect  the resultant cosmological redshift!. After collecting evidence for many years, Halton Arp maintains that extragalactic redshifts are not caused by an expanding universe.
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A 3-spherical geometry for the Universe was once proposed by Einstein and is still held by others.
For example, a 3-spherical geometry could explain Big Bang evidence, such as:
  • The redshift of galaxies.  Explained by geometrical lensing from the geodesics of S3.
  • The CMB.  Could be caused by diffused light from geodesics originating from “behind” earth’s antipode, etc.
I’m sure there is more evidence for the Big Bang, but the two above are the most cited.
The reason I’m considering that particular geometry for the Universe is that the existence of matter-waves can be attributed to S3 motional geometry.
One more thing, the dimensions of the 3-sphere are assumed to be spatial and do not include time as a dimension.  The fourth dimension of the hypersphere is unobservable therefore unknown.
If that’s the case, the need for a Big Bang becomes questionable.
Your comments, please.
Bernardo.
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Don't spam other people's questions Adrian, go away and work out the proofs for the questions you've been asked first.
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As a theoretical cosmologist, spectral index, running spectral index and scalar to tensor ratio are some of the things one can easily calculate for the model we devise. But it comes very handy to plot them on top of the distribution that is usually obtained by running CosmoMC on Planck data. Can someone describe how these plots are obtained and what is quickest way to reproduce the such as fig.9 in the link attached, without divulging oneself into the details of Planck data analysis. 
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there is some programs allow you to take the numerical values  from the scientific graphs like  r and n_s in planck results  , then you can  re-produce this contours by matlab or any other program, see for example "dagra" , it's simple and good programm I'll add the link of home page of the program
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I think that inside a reactor one can obtain neutrons of different energies. My question is if it is possible to create two sources as in the picture?
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Dear Sofia!
The fission neutrons have different energis like β-particles. The question is how to separate neutrons. I would say you can lead two neutron-beams through differently thick shilds of moderator. The two neutron beams will show two spectra of energy.
By the way the picture is idealised. To shield neutrons absolutely is nearly impossible.
Regards
Hans
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It has been deduced from WMAP and Planck observations that the expansion of the universe is accelerating. This would mean that the present pressure in the  universe is negative. Do we have any knowledge of the value of this pressure or of its order of magnitude (be it obtained by calculation or by measurement) ?
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Dear Guibert,
yes, we do. It's a trivial exercise in cosmology. However, one has to be careful because what is called "pressure" in cosmology is often given in units of an energy density, which is however just a shortcut to avoid writing too many constant factors.
In any case, our current Universe (i.e. its energy density) basically consists of radiation (sub-per mille level), non-relativistic matter (dark and non-dark, about 31.5%) and its main component dark energy (68.5%). Out of these, radiation has pressure but its amount is negligible. Non-relativistic matter is pressureless and dark energy has, as you correctly say, negative pressure.
Thus to an excellent approximation the total pressure of the Universe can be set equal to the partial pressure p_DE in dark energy, which is just minus the energy density rho_DE in dark energy. The latter is given by 68.5% of the "critical density" rho_crit = 1.878e-29 g/cm^3 x h^2. h=0.67 is the reduced Hubble constant (both rho_crit and h are measured, not only by Planck or WMAP, but also by further astrophysical observations - although typically less precise). Turning units of g/cm^3 into Pascal gives a factor of 9e19, so that the total pressure in a cm^3-piece of the Universe is given by:
p_Universe = -rho_DE = -0.685 x 1.878e-29 x 0.67^2 9e19 Pa = - 5.2e-10 Pa.
Note that in cosmology we always talk about densities rather than absolute quantities - it would not make sense to translate this value into a "total pressure" of the Universe, since we don't know the size of the Universe and also because there is no way to measure such a total amount. We also don't use SI units, but in any case, the message is yes we do know the pressure of the Universe because we have measured it.
Best regards,
Alexander
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Under what natural processes could stellar formation have occurred after the initial singularity but prior to a cosmic inflation event?
Assume this is the scientific actuality, so it is not a question of if it could have occurred but how it could have occurred.
Assume  CR does not indicate any ongoing cosmic expansion. 
Thank you,
r
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Dear Colleagues,
 I send you the paper
I. A. Urusovskii, Multidimensional   Treatment of the Expanding Universe,
 Physical Science International Journal, 4(8): 1110-1144, 2014, 
Containing answers on questions of Dr. Robert Oldershaw (see the Figure 6 in the paper).
Best Regards,
I. A. Urusovskii
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Is it possible to have a world that does not change its scale factor a(t)? Physically there is evidence for it, a(t)=Constant ? Is it means a possible world with a constant radius?
Cosmologist
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The requirement of a static universe was what inspired Einstein to introduce the cosmological constant. He found a solution, but it is known to be unstable. I don't know if there exist any stable static solutions, but they would anyway not correspond to the universe we live in. So why bother?
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I am interested by some connections between cosmology, gravity etc with life sciences, biophysics or whatever. I will be appreciative if you can give me some initial starting points with articles, textbooks etc dedicated to my interests.
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see arXiv 1311.6328 quant-ph.
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Giant black holes are suspected be located at the center of spiral galaxies.
In our galaxy, it was observed that stars located near the center have elliptical trajectories that correspond to the presence of a mass at the focus of the ellipse.
Does anyone know what are the observational elements requiring that this mass must be a black hole?
Why could not it be, for example, a dense cloud of gas?
Thank you for any element of information.
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From the orbits around the central mass in our galaxy it can be concluded that the central mass is about 4 million solar masses (cf. Sagittarius A*).
The Schwarzschild-radius r=2GM/c^2 of 4 million solar masses is roughly 10^10m.
A star is orbiting the central mass at a closest distance of round 10^13 m, the radius of the central mass must be much less, otherwise the star would collide with it. 
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I noted that ultraluminous X-ray Source (ULX) luminosity is usually determined by calculation from flux and host galaxy's distance measurement. I want to know the idea of determining ULX membership to a particular host galaxy, since there maybe no counterpart observation in other bands.
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ULXs are compact, off-nuclear, X-ray sources with X-ray luminosity > 10^39 erg/s. If there is no counterpart detected in other wavelength (lets say Optical), we can possibly rule out the association of foreground stars or background AGNs to ULXs (unless they are very faint or highly obscured). Since these objects (stars/AGNs) were dominantly emit in visible wavelength and can be easily identified in the optical observations. The flux ratio (X-ray-to-optical) of these objects will have specific range, which can be used to differentiate the background/foreground objects from ULXs.
(See Stocke et al 1991, Lotz et al. 2004, Jithesh et al 2011) 
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We have learnt from the big bang cosmology that all the particles was created after the big bang explosion. My question is that whether these particles was created from the energy released due to the big bang? If yes, the energy density must be decreases during the course of expansion as it is continuously converting into masses or matters. Again if it happens so, the mass of universe must be increasing with time or expansion.
Please some give some light on it. I'm working on a solution of Einstein's field equations and I got an expanding solution with an initial singularity. As the time increase to future, its mass and radius increases. So I need to explain the increase in mass with time.
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Dear Amrit Sorli, Are you suggesting Steady State Theory of Universe? Than how can you expalin CMRB?
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Over the years, many physicists have wondered whether the fundamental constants of nature might have been different when the universe was younger. If so, the evidence ought to be out there in the cosmos where we can see distant things exactly as they were in the past.
One thing that ought to be obvious is whether a number known as the fine structure constant was different. The fine structure constant determines how strongly atoms hold onto their electrons and is an important factor in the frequencies at which atoms absorb light.
If the fine structure were different earlier in the universe, we ought to be able to see the evidence in the way distant gas clouds absorb light on its way here from even more distant objects such as quasars.
That debate pales in comparison to new claims being made about the fine structure constant. In 2010, John Webb at the University of South Wales, one of the leading proponents of the varying constant idea, and a few cobbers said they have new evidence from the Very Large Telescope in Chile that the fine structure constant was different when the universe was younger.
While data from the Keck telescope indicate the fine structure constant was once smaller, the data from the Very Large Telescope indicates the opposite, that the fine structure constant was once larger. That’s significant because Keck looks out into the northern hemisphere, while the VLT looks south.
This means that in one direction, the fine structure constant was once smaller and in exactly the opposite direction, it was once bigger. And here we are in the middle, where the constant as it is (about 1/137.03599…)
So, do you think that fine structure constant varies with direction in space?
Refs:
arxiv.org/abs/1008.3907: Evidence For Spatial Variation Of The Fine Structure Constant
arxiv.org/abs/1008.3957: Manifestations Of A Spatial Variation Of Fundamental Constants On Atomic Clocks, Oklo.
Included here you can also find a 2004 ApJ paper by John Bahcall, who is a proponent of varying fine structure constant. (URL: http://www.sns.ias.edu/~jnb/Papers/Preprints/Finestructure/alpha.pdf)
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Since the value of the fine structure constant has been found to be the resultant of a combination of 4 other constants: alpha= e2 /(2 eps_0 h c), that can mutually define each other, this means that if alpha should be found to have a different value, this would also mean that at least one of the other related constants also has a different value.
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If I'm correct that images of distant stars and galaxies can show multiple celestial objects at massively differing distances away and therefore some points of light are effectively representing images from differing moments in the past.
If those different points of light are actually derived from differing moments in time, how do observers/recorders represent the difference in time between them visually or analytically?
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Keith your initial question appeared inchoate, but looking at the responses it appears that you are mainly concerned with how distances for astronomical objects are discerned and the uncertainties. There is a general concept in basic astronomy of the distance ladder. We establish distances to nearby objects (through trigonometric parallaxes), determine new "standard candles," and expand the process until we arrive at red shifts for the most distant objects, which are luminous galaxies or quasars at cosmological distances. The recording in these processes involves first astrometry (careful measurement of positional shifts on the sky), then relative brightness of stars, clusters of stars, and galaxies, or galactic nuclei (involving careful measurement of luminous flux, and making use of the inverse square diminution of light with distance) and spectroscopy (to register the Doppler shift of receding galaxies).  The development of individual "standard candles," one of which --- the Cepheid pulsating variables --- was mentioned above, involves a much longer discussion, but I get the idea that you are not so much interested in those details. As to distance resolution, yes, as noted previously, in general the greater the distance, the greater the uncertainty.  To give you a peg, for nearby objects in the Sun's vicinity, out to a few hundred parsecs, the uncertainty is of the order of a parsec.  Does this do it?
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It would rule out vacuum being the source of the CBR
(or confirm)
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You should add Bose-Einstein condensation to the list of topics for this question.
How do you think anyone could do experiments which requires microKelvin temperatures (or cool matter below nanoKelvin temperatures), if the vacuum behaved like a 2.7 K reservoir? 
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Flux from any object drops with increase of red shift. As the object is  in higher red shift,  it looks fainter. But in the sub-millimeter band galaxies get brighter with increase of z.  The explanation is given as negative 'k-correction'. Can you explain it?
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As an aside, this concept applies to any object with a steep SED, and is brighter at longer wavelengths.  But also, the hard and fast rule of "further away, fainter, harder to detect" is violated by another class of observations.  These are observations of the so-called Sunyaev-Zel'dovich Effect in clusters of galaxies.  This is caused by a distortion in the cosmic microwave background on arcminute angular scales because the CMB photons are inverse-Compton scattered by hot (10^7 - 10^8 K) plasma in the potential wells of galaxy clusters. As the CMB photons pass through galaxy clusters, they are preferentially upscattered to higher frequency, leaving a "hole" at lower frequencies.  
This effect is also "redshift-independent", to the extent that the detectability of these objects at high redshift is essentially the same as if they are at lower redshift (modulo the effect of the change in their angular size due to distance, and universal geometry). This is because the objects that are further away are subject to a CMB that has a higher energy (since the CMB energy spectrum is "hotter" at high redshift), and that exactly cancels the effect of diminution of flux as f(z).  Thus the "flux" of this effect, which is really a shifting of the spectral energy distribution of the CMB from longer (> 2 mm) to shorter (<2 mm) wavelengths, is independent of z.  Thus an observer can measure similar "flux decrements" in the CMB, or "flux increments" at longer or shorter wavelengths respectively, which are identical for objects at z=2 as for objects at z=0.5.  This makes the effect a powerful tool for studying structure formation, and its evolution over time.  This effect is currently being exploited for just such studies by the South Pole Telescope, Planck Surveyor, Large Millimeter Telescope, and other mm and sub-mm interferometers. 
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According to Mukhanov's "Physical foundations of cosmology" (page 230), to solve the Horizon and flatness problems, the rate of change of the scale factor today should be greater than the rate of change at the beginning of inflation. However the attached diagram shows that it's the opposite. Could someone please clarify this issue for me?
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Ali, models are not "wrong" since they are adjusted to fit data. Ptolemy model was not "wrong" either, it fitted data. These kind of models are a necessary step in the process of discovering because they organize data and reveal their global properties. But they are not necessarily "logic", their goal is to obtain equations that fit data and how that is achieved is not really important. You do well in trying to build a logic path but you will find out that sometimes it does not exist in these kind of models - don't give too much importance to it, these are just mathematical models. Nor you should believe that dark matter is a physical entity, it is just an ad hoc parameter; or that really there was a "cosmic inflation" or even a Big Bang - we know nothing of what happened before the CMB, the BB is just a mathematical extrapolation.
The standard model is the best model available, but this does not mean that it is perfect, or "the truth". In Physics it is always like that, a going on discovery process; the cosmological model, the atomic model, QM are just the best models available in each field but they all have difficulties. The concepts of "right" or "wrong" do not apply, only the concept of "best model available". As people tend to classify things in right and wrong, the difficulties of the models are not usually spoken because then people would fall in the simpleton conclusion that they are "wrong". 
Note, however, that there is a kind of model in relation to which the concepts of right and wrong apply, the concept of falsifiabilty applies: a model with no ad hoc parameters, no unknown entities. These models cannot be adjusted to data, either they fit it or not. Like Newton's model (that is why he said "hypotheses non fingo"). To obtain such a model is not an easy task...
I am saying these things because obviously you have a clear mind and you seem able to scope with the complex nature of things... and so it is possible that you will later be able of giving some important contribution to improve the models - eventually a model with no unknown entities.... Who knows?
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Fleury, Dupuy, & Uzan reported in Phys. Lett. (2013), that it is possible to interpret the Hubble diagram in the context of nonhomogeneous universe. They wrote as follows:
"In the standard cosmological framework, the Hubble diagram is interpreted by assuming that the light emitted by standard candles propagates in a spatially homogeneous and isotropic spacetime. However, the light from "point sources"--such as supernovae--probes the Universe on scales where the homogeneity principle is no longer valid. Inhomogeneities are expected to induce a bias and a dispersion of the Hubble diagram. This is investigated by considering a Swiss-cheese cosmological model, which (1) is an exact solution of the Einstein field equations, (2) is strongly inhomogeneous on small scales, but (3) has the same expansion history as a strictly homogeneous and isotropic universe. By simulating Hubble diagrams in such models, we quantify the influence of inhomogeneities on the measurement of the cosmological parameters. Though significant in general, the effects reduce drastically for a universe dominated by the cosmological constant."
So do you think that Swiss-chess model can be made close to observation? What do you think?
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@Alexander: Thanks for your comments.
@Mohamed: thanks, yes I have read at a glance your paper, but as far as I know, your paper does not discuss  light emitted by standard candles. Your further comments are welcome. thanks
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The early models of decay can be found in the works of Friedrichs (1948), and Feshbach (1958). In these works it is said that the intra-nucleus dynamics of the particle(s) to be emitted, is influenced and becomes coupled with the dynamics of the same type of particle(s) in the environment, i.e. in the states belonging to the continuum of energies in the environment.
So, in the above works a total Hamiltonian HT is built, comprising the Hamiltonian of the parent nucleus, the Hamiltonian of the continuum, and the coupling Hamiltonian.
Referring for simplicity to the α-decay, HT should comprise the Hamiltonian HB whose eigenstates are bound states of α, the Hamiltonian Henv of the continuum of α-levels of energy of the environment, and a coupling Hamiltonian HC. The effect is said to be a widening of the bound states of α into resonance states, which are no more of a sharp energy but have a width Γ, and therefore have a half-life proportional with ħ/Γ.
I am asking three questions:
A. As the environment is in VACUUM state in the beginning of the decay, what can move in the vacuum s.t. the movement of the α inside the parent nucleus, can get coupled with? What moves in the vacuum?
B. I know that the nuclear decay has some similarity with the de-excitation of an atom, but in atom de-excitation the electron is influenced by an e.m. field. To the difference, in α-decay one cannot say that the α inside the nucleus is influenced by the α outside. We don't know an α-α field. So, which field can couple the intra-nucleus α with the α-vacuum?
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Dear Sofia,
Feshbach approach is one among the languages, which can be used for understanding of decay phenomenon. It is aimed to build a universal formal  tool for resonance description in multi-particle case first of all. In more intuitive and simple "one-dimensional" case (described by Gamow via decaying quasi-stationary states in case of alpha-decay) Feshbach formalism could be too formal and somehow misleading (if you are seeking for more intuitive explanation). The classical book A.I. Baz, Ya.B. Zel’ dovich, A.M. Perelomov, Scattering, Reaction in Non-Relativistic Quantum Mechanics. Jerusalem, 1969. containes very intuitive and mathematically strict description of decay process and consept of quasi-stationary states in terms of fully hermetian approach.
As for the decay due to "interaction with  environment", this is a typical multiparticle problem (similar to excited atom de-excitation via interaction with radiation EM-field).Multi-particle (or multi-channel) decay is specific due to the fact that one of the subsystems ( which is bound, like electron in atom) can interact with another  subsytem (which is unboud and can escape to infinity like photons ). Alpha-decay in its essential part is one-particle problem, so the notion of "interaction with environment" is artificial and could be used here only formally. "Environment" and "bound alpha-particle"  in such one-dimensional problem are simply  spartially separated regions (outside the potential well and inside the well) both accesible for a quantum particle. The formal  devision of  a one-particle Hamiltonial into parts, responsible for bound states  and free motion  outside the potential well is implementation of projection method, widely used by Feshbach in multi-particle case. Its application to well-understood one-dimensional case is to illustrate the Feshbach method on a simple example, but not to give the most straightforward and intuitive way of understanding one-dimensional decay. So one should not take the term "interaction with environment" in one-dimensional case literally, it has specific abstract sense here. In particular, there is no alpha-alpha interaction.
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Gravitation
Delta\tau_g = \frac{g}{c^2} \sum_{i=1}^{k} (h_i - h_0) \Delta t_i
How the difference between 0m and 5000m on Earth should be today (after for example 4.5 billion years):
\Delta\tau_g = \frac{~10}{9*10^{16}} (5000m - 0m) 4.5*10^9 years = 21.9 hours
Following the theory, shouldn't we see a difference of 21.9 hours between two picture of the sky taken at 0m and 5000m?
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Have a look on my book "ESSAI (version V2) - L’univers pourrait-il être un réseau 3D et la matière ordinaire en être des singularités topologiques ?". You could find some interesting answers!
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The observed Lithium abundance is in disagreement with the standard big bang model. What are the possible solutions to the problem?  How much the observations are reliable in this case? Is it possible to exist a method of destruction of Li that we don't considering or it is beyond standard model phenomenon?
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Not everybody thinks that the standard Lambda-CDM theory of cosmic structureformation is a good idea. Recent patches to the theory propose that the strongest signal in the COBE/WMAP/PLANCK background maps is baryonic accoustic oscillations, but nobody has the courage to ask, "If the baryons dominate structure formation scenario, what about turbulence in the baryons?" Indeed many find that the background overall obeys fractal mathematics and is turbulent in origin at z = 1100. See papers by Carl H. Gibson (UCSD), Sylos Labini (Rome), and Bershadskii (Tel Aviv).
If that is true, and turbulence traces back to the era of atomic element formation, the standard assumption of a homogeneous Universe expanding in thermal equilibrium are in question, and in particular the Michael Turner and more recent calculations of thermal equilibrium elemant formation are questionable. For example, when the temperature of the hj-z universe was 10^7, local heating of a volume would produce atomic fusion with its very strong 10^12 temperature dependence. This would cause runaway fusion and solve the puzzle of the Spite minimum in atomic abundances, the fact that we do not find any Pop III stars at any redshift,  or anywhere in our Galaxy or Halo.
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Space of Universe is static! Yes or no?
Question: Are there any observations that do not fit into the model static space of Universe, are there any theoretical obstacles to the existence of such a model?
I assume that the Universe is eternal, infinite and static, it is not expanded and not curved, it is possible to construct a preferred inertial frame of reference in which the CMBR is most isotropic. The matter in this space evolves, but the average density of matter and energy (in large enough volumes) fluctuate within a rather broad range.
The light in this model is "tired", the speed of light depends on the optical density intergalactic medium. Gravity is also "tired" t.i. weakens a little faster R2. The energy of destroying matter goes into the surrounding vacuum. The excess energy from the vacuum give rise to new particles of matter.
I state that all the observed cosmological effects can be explained in such a Static Model of the Universe.
See attached "Basic_Cosmological_Formula_1_En.pdf"
Dear colleagues, I do not ask, what are the problems faced by other theories (though I would be interested in your opinion on that. The General theory of relativity is not applicable to the entire space of the Universe).
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Victor,
Bravo,  Well said.  If logic has no place in science than I have no need to comment on anything.  There are too many illogical arguments that have a prominent place in our science today to have anyone think that they are right or wrong and truly believe it.  If we cannot move back to a place in science that brings us the truth then we are all in trouble.
Science has made some very big advancements in the last one hundred years.  If Albert Einstein and others had not seen the quanta as a problem that had to be worked on there would not be computers, or cell phones or so much more in the world (maybe this is the problem) but it has also lead us in some trouble sum directions as far as science goes.  If we do not understand the Quanta and its physical implications then we are doomed to fighting over illogical verses logical arguments in science.  This will not bring us any closer to the real problem.
If one of these so called approaches to the answers of today's concerns in science is correct then it would have been proven by now and have no questionable concerns over its truth.  This is however not the case.  All the science that we have come up with works in a limited range of situations and is not the theory of everything as most people think we should have.    
In a logical sense we need to take a step back and look at all the discoveries that have been made.  Then stop looking at the order of the discoveries and start looking at what happens when we do not care about the order of discovery but what the preponderance of all of it means.  This would have to be with the ability to say to yourself and other scientist in the world, "forget what you thought you knew and look at it with fresh eyes.  This brings to mind a quote from Socrates almost 2500 years ago.
    Socrates said it best, "Learning was first and foremost a process of discovering what it is we wrongly thought we knew, of first exploring ignorance before going on to knowledge. Merely adding bits of wisdom to a mass of foolishness will not make people wiser. It will only increase the danger of their Ignorance."
At this point in science we are dangerous.
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I am supervising an undergraduate student doing a final year research project in statistics. For her project she would like to look at cosmological parameter estimation using Monte Carlo Markov Chains. One problem is finding relevant data that she could use.
Does anybody know of any freely available data that would be suitable for the above-mentioned project?
Thank you in advance to anyone able to help.
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I've asked this question once; want to be more specific now; hope will be luckier this time around. According to the original Gamov-Alpher-Hermann theory, the CMB temperature goes down with time "t" as t^(-2/3).  A recent discovery of accelerated expansion of the Universe apparently is changing this. So what is a new dynamics of that temperature?
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According to thermodinamics T is inversely proportional to the scale factor, In the standard model previous to SNe1A "accelerating" universe your equation was considered right. Now, a more complex behaviour as emerged as standard. From my own work, the steady flow model, you get T inversely proportional to t for almost the entire history of the Universe, with some interesting implications...
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A glance through our cosmic neck of the woods reveals that matter in the Universe is distributed in a highly structured fashion, why is it so?
Regards,
Bhushan Poojary
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Dear Daniel; I agree that this is an important question, and of course it has been addressed, best by Theo Nieuwenhuizen in his paper "Model for common growth of supermassive black holes, galaxy bulges, and globular star clusters; Ripping off Jeans clusters, in Europhysics Letters 97, 39001. This paper explains and derives the Schmidt-Kennicut law, which is a relationship between the velocity dispersions of all galaxy bulges and the mass of the central super-massive black hole.
Also available on astro/ph, this paper describes in a statistical mechanics calculation the answer to your question on galactic scales. Other papers describe separately the formation of star clusters and the primordial rogue planets. In the planetary case, gas forces produce pressure to form a dark mini-star with a structure of an n=1.5 polytrope. The globular cluster case is related, but the gas particles are now the rogue planets, but we know that globular clusters last the age of the Universe, and their stellar dynamics is well understood.
In this picture, all of the structure formed at the z = 1100 plasma neutralization is concentric, meaning the Galaxy is made of Jeans clusters made of primordial planets. The galaxies in turn are in clusters within superclusters, which takes you to Gpc scales.
As a side comment, the problem with galaxies is not their collapse, but rather that measured rotation curves seem to require the presence of so much dark baryonic matter.
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I can´t find anything other than the standard expression valid BEFORE recombination which does not depend on the ionization fraction, or expressions for AFTER the precipitous fall in the sound speed after last scattering. Has anyone modelled that "precipitous" fall (in either sound speed or pressure) in detail as a function of the (small and falling) ionisation fraction? 
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Sound speed during recombination depends on wavelength. A critical barrier is the photon scattering length. Roughly: over greater wavelengths the speed of sound keeps relativistic, below it is thermal. A more detailed reply can be deduced from a (slightly dated) paper of mine: S.A. Bonometto & F. Lucchin, Astron.& Astroph. 43, 189 (1975) "Acoustic Modes and Gravitational Instabilities in the Early Universe".
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Space expansion is not absolute, it depends on the length unit – using the co-moving length unit, space is invariant. So, how do we know whether is the space that expands or the standard length unit that decreases?
One may thing that if the length unit were varying, physical laws would not hold. However, that is not true! One can define a comoving system of units where space is invariant and physical laws hold, and all constants keep invariant. The problem is as non-trivial as the old question of knowing whether rotates the whole universe or the little Earth, which inspired Galileo.
Furthermore, there is a suspicious resemblance between Big Bang model and Ptolemy model: both have one unknown entity to drag stars around or away (celestial spheres and dark energy), another to explain local motions (epicycles/deferent and dark matter), both are only valid at distance and both consider that the nearby universe is dominated by matter while the distant one by unknown entities.
In my opinion, we have to give a scientific answer to the above question and not be ruled by presumptions, as it happened in the similar geocentric case. I would like very much to know your opinion: do you consider this question important? Do you have an answer to it?
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Alfredo: your question "Does the expansion of space increase or decreases the unit length?"  May be answered considering "replication" of the unit length, the Plank´s length, so that there is no increase or decrease of the unit length: it is not afected by the expansion of the universe. It just replicates. Today it has replicated about 10^61 times, that is how expanded is the universe around us now.
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It is mentioned that, Some researchers in March last year had used a telescope at the South Pole, namely the BICEP2 telescope, which studied a small patch of sky in detail above the South Pole. They discovered primordial gravitational waves. This in scientific circles was a very big deal, on the level of a "big bang" look at the birth of the universe. New Scientist compellingly described it back in March, "showing us what was happening in the first slivers of a second after the big bang."
However, reported Jacob Aron in New Scientist on Friday, "details of a new analysis of their results have leaked, and they seem to reveal that galactic dust is the likely cause of their observations.".
They still have not ruled out inflation theory yet , but what if we are not able to detect it at all, What other alternative theory would replace inflation theory in case if inflation theory is proved wrong.
Regards,
Bhushan Poojary
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The big bang theory does not precisely fit observations, which is surprising due to how tunable inflation is. By tunable, I mean it can fit almost any universe by adjusting its many parameters.
1. The quadrupole has a lower magnitude than predicted by big bang cosmology.
2. The alignment between the quadrupole and octupole are unexplained in big bang cosmology.
3. The big bang theory does not predict the observed hemispherical power asymmetry.
4. The big bang theory does not explain the large cold spot(s).
5. Relative to the big bang framework, the sigma_8 parameter predicts 2.5 times more clusters than observed in both optical or x-ray surveys.
The vast majority, if not all of these, can be explained from a relatively new theory published in 2014. In short, the CMB would originate from the center of a cosmological-scale gravitational potential, where it is projected locally due to gravitational lensing (hence the hemispherical power asymmetry). That is, Earth would be distant from the center of such potential, causing the CMB to undergo gravitational redshift. This theory also predicts B-modes, which provide a >3.5 sigma fit at large-scales (using zero tunable parameters).
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Does it imply that if the theory did not allow calculating values of the given quantity in reasonable time, then this theoretical quantity would not have a counterpart in physical reality? Particularly, does this imply that the wave functions of the Universe do not correspond to any element of physical reality, inasmuch as they cannot be calculated in any reasonable time? Furthermore, if the ‘computational amendment’ (mentioned in the paper http://arxiv.org/abs/1410.3664v1) to the EPR definition of an element of physical reality is important and physically meaningful, should we then exclude infeasible, i.e., practically useless, solutions from all the equations of physical theories?
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Charles, no, it is done for momentum meausurement, I have given the formulas, of course, one needs the cofiguration of the measurement device as well as the full wave function for this too, and, again, this is not speculation but the prescription, the necessary consequence of the dBB equations, and this is well-known since Bohm's paper. Because this extension from position measurement to all other quantum measurements was the main new result of Bohm's paper in comparison with de Broglies original theory. 
Only repetition of already rejected arguments, so it seems time to finish this discussion. Its already clear that you have no counterarguments against the points I have made, but are unwilling to accept anything.  Bye. 
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The reports by Tifft on quantization of galactic redshift are well-known to astronomers. Read for example http://www.vixra.org/abs/1309.0011. See also a recent review on redshift theories by Marmet at http://www.marmet.org/cosmology/redshift/mechanisms.pdf
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I don't have articles on Tifft's quantization, but I will send you two of my articles on static models.
I think that the space of the Universe is not expanding. Test Tifft's quantization will show it, because in the framework of GR the distance between galaxies previously had to be less than it is now. Therefore, in GR dependence should be approximately inversely proportional to z.
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Kaluza–Klein theory is theory which uses 5th dimension to unite Gravity with Electromagnetism.
does this theory have any short fall or is it perfect?
If someone can help me with original article it would be nice of them.
Regards,
Bhushan Poojary
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There is indeed a problem with Kaluza-Klein theory as it is formulated (i.e. 4D space cross a circle). When one dimensionally reduces the theory to 4D, one indeed obtains General Relativity + EM, although the 5D theory has an instability in that the radius of the extra dimension is unstable: small fluctuations will cause it to pinch off or expand outwards. This is typically true of any compact extra dimensions and in order to stabilize them you need to introduce various fluxes, which requires adding other matter fields to the theory. If the goal is to get matter exclusively from geometry, then adding matter in order to stabilize the geometry runs counter to that goal.
What's more is that we now know that EM is unified with the weak nuclear force, so why should we be interested in unifying gravity only with EM and not with the electroweak force? At the time of Kaluza and Klein, the weak nuclear force was not very well understood and it was certainly not known that it and EM are different manifestations of a single force. Nevertheless, the idea is intriguing that the particles we know and love can be obtained from dimensional reduction of a higher dimensional theory.
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Can we get any help of dark energy momentum tensor in f(r,t) theory?
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Thank  You So much...for the valuable answers!!
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Cosmological interactions are often related to the energy density of the interacting system or to their time derivatives. Is it possible to relate the interaction between spins of a fluid with its energy density? Or with an arbitrary function of its time derivatives?
In other words, can a cosmological interaction  be derived from the interaction between spins of a cosmological fluid ?
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Thanks Farid.
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In a rather old paper, Michael Heller argues that in certain cases it is possible to remove the initial singularity from cosmology models. He discusses b-boubdary and noncommutative geometry. So what do yo think?
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I think that nature has ways to avoid singularities. E.g. the two flows of air above and below an air foil, the section of a wing in an aircraft, have different speeds at the end tip: faster above than below: then viscosity enters into the picture and vortices appear to remove the "mathematical" discontinuity. Same happens when we have a supersonic flow that has to stop due to the presence of a solid object: then a shock wave is produced and the flow behind the shock is subsonic and no discontinuity appears. In the case of the initial stages of the universe, dealing with a theory with continuous variables like general relativity, we arrive at a "mathematical" singularity. Then quantum mechanics enters into the picture ad no singularity is in the picture. I believe that in nature there are no zeros nor infinities, no singularities. Nature is already "defined", and we have to understand it. Nature does not necesarily has to  follow our mental constructions.
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The new discovery from the BICEP2 indicated that the inflation may be happened for a longer time than predicted before. In addition to that, the high values of gravitational waves detected indicated that there is a larger force of expansion than thought before. Is this an indication that inflation may have kept happening until the recent discovery and it may be responsible for the detected expansion?
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If I may add: has BICEP2 actually detected primordial gravity waves? No to  that one too. (short answer).
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I read somewhere that Einstein's equations may be expressed in terms of Klein-Fock-Gordon equation, but i am not sure yet how to do that.
In a paper, Fiziev and Shirkov discuss solutions of Klein-Fock-Gordon equation and its implications to Einstein's equations. In effect, this may imply that Einstein's equations have wave-type solutions.
What do you think? Your comments are welcome.
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Thank you Stam, for your answer. Best wishes
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As far as I know in order to explain the horizon problem in cosmology, two major theories have been put forward viz, inflation and VSL (varying speed of light). My question is this, by detecting primordial gravity waves by BICEPS 2, thus proving the inflation theory, w