Analyzing the candidacy of gravitino as constituent particles of
Shreeji Kumawat 1
1 Physics student at St. Xavier’s School, India
Abstract: Dark matter makes up about 85% of our universe, a fact supported by both theoretical
and observational evidences, yet we are still searching for theories to accurately describe its com-
position. Unlike regular baryonic matter, dark matter refuses to interact with electromagnetic
radiations, making it more evasive to detect. Several theories have been proposed to explain it’s
origin, most popular ones suggesting WIMPs, Light bosons and neutrinos as constituting parti-
cles, although none of them have been successfully proven. In this paper we focus on establish-
ing gravitino, a type of hypothetical particle in quantum theory of gravity, as a viable candidate
for constituting dark matter. We begin by highlighting the basic assumptions and principles re-
lied upon, such as the model & Effective Field Theory (EFT), and then proceeding to
gradually point towards the proposed relation between dark matter and its decay widths to
standard model particles, particularly photons. In a key part of this paper, attempts have been
made to indicate that the proposed energy possessed by photons after gravitino decay in our
model actually coincides well with the real time energies of gamma ray bursts GRBs) observed
just after the detection of gravitational waves. In depth analysis of data made publicly available
by LIGO and Fermi GRB observatory is done in order to arrive at this result. In conclusion, we
calculated and demonstrated a close relationship between the observed and theoretical value of
GRB energies, thus implying that gravitino could well be considered as a constituent for dark
Keywords: (Gravitons) (Dark Matter) (Quantum) (Gravity) (Gamma Ray Bursts) (Gravitational
Dark matter is a hypothetical form of matter which makes up to 85% of all matter in
our universe, according to the standard LambdaCDM model . It does not absorb, emit
or reflect any kind of radiation and does not even loose kinetic energy to heat except in
one inefficient process of gravitational ejection. This makes it difficult to detect with tra-
ditional techniques and instruments, forcing us to rely on advanced theoretical ap-
proaches for its detection, majority of whom rely on measuring its gravitational effect on
nearby objects. This is synonymous to locating a black hole by observing the behavior of
baryonic matter around it. Even though its detection has not yet been achieved, we have
good reasons to believe it exists. Our currently accepted theory of gravity gives almost
nonsensical answers to various astrophysical equations unless an invisible yet large form
of matter if accounted for.
As such, the need for DM was recognized and it was defined to be ‘matter that is not
visible but whose energy density scales with the inverse cube of a scale factor’. This im-
plies the simple relation:
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where is energy density and α is a scale factor . Having sufficiently introduced
DM, we now proceed onto listing the various reasons and methods that prove its undeni-
able existence and imply its crucial role in the formation and evolution of our universe.
1.1. Theoretical Evidences
The first hint towards existence of DM was provided in 1933 when Fritz Zwicky
analyzed the Coma Cluster of galaxies with Virial Theorem . The theorem can
be stated as a relation between a system’s total kinetic energy and its virial:
Modifying the theorem to include gravitationally interacting masses as shown
allowed Zwicky to estimate the mass of the cluster in relation to motion of its
galaxies near the edge. But when he calculated the mass again using luminosity
and the number of galaxies, he found the two values differed by 400 times, show-
ing that some large amount of matter that wasn’t contributing to luminosity was
present and affecting the overall cluster motion.
Rotation curves for the andromeda galaxy were observed by W. Babcock in 1939
soon after, reporting mass-luminosity ratio of 50:1 and a peculiar rapid rotation
motion in outskirts . This result was later used by Jan Oort to hypothesis ex-
istence of DM that caused invisible attraction. Vera Rubin and Kent Ford also
measured the velocity curves of spiral galaxies with spectrographs to a great pre-
cision, proposing that most galaxies contain DM about 6 times greater than reg-
ular matter .
A majority of proofs that followed later focused on galaxical rotation curves, in-
sisting that from Kepler’s second law it is expected that rotation velocities de-
crease with distance from center. But observations show a flat curve (Fig. 1)
meaning that mass distribution must not be regular. If Kepler’s laws are correct
then a non-luminous matter must be present in outskirts of such galaxies. Fried-
mann solutions for structural formation of our universe also show that if there
were only observable matter, galaxies and clusters would not have evolved due
to slow density perturbations . All these rationales shown above are used to
accept DM existence based on theoretical analysis of known laws.
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Figure 1. This shows the galaxy rotation curve as expected vs. its observed value.
1.2. Observational Evidences
Our conceptual reasons for DM presence are also supported well by numerous
strong observational verifications. Radio astronomy showed early on that half-
dozen galaxies spun too fast in outer regions, meaning some sort of gravitational
attraction was there to keep their stars in orbit . There are several methods to
measure a galaxy’s mass, using either scatter in radial velocities or X-ray spec-
trum from hot centers to estimate density and pressure. Gravitational lensing is
a method where galaxies lying between distant quasars and observer act as a lens
bending light. The magnification observed gives us an estimate of mass causing
distortions. All above mentioned methods arrive at a common agreement that
DM exceeds visible matter in abundance by 5 times .
Cosmic Microwave Background is also by affected by DM in terms of its gravita-
tional potential and effect on velocity & density of ordinary matter, thus imply-
ing evolution of matter perturbations with time on CMB. Using sky map aniso-
tropies, an angular power spectrum can be formed to show densities of baryonic
and DM . This spectrum fits perfectly with results from LambdaCDM model
but proves difficult to explain with Newtonian mechanics alone.
Lastly, in a long list of experimental conformations, we lay emphasis on the Bul-
let Cluster, which was recently formed as a result of a two-galaxy collision. Its
apparent center of mass differs vastly from baryonic COM, an effect lucidly ex-
plained by DM models but almost unaccounted for if one relies solely on modi-
fied gravity .
2. Quantum Gravity
The foundation idea of Quantum Gravity is that gravity arises from quanta scaled
packets of energy called ‘gravitons’ which do not exist in space, but are space themselves
. These mediate the force of gravitation between particles and are responsible for the
bend in space-time in presence of mass. They are the carries of hypothesized gravitational
fields, are massless and electronically neutral, much like the analogous photons that me-
diate electromagnetic interactions. In the standard model of particles, it is theorized to be
a spin 2 boson particle because its fields travel at speed of light and are effective at long
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range. If in the near future the vacancy of a massless spin 2 particles is filled, it is expected
to a graviton .
But the candidate we propose for DM is gravitino, a close partner of graviton in the-
ory of supergravity. This is a theory that deals with the combination of general relativity
and supersymmetry in areas where quantum effects of gravity become considerable on
relativistic scale. Supersymmetry proposes a space time symmetry between two classes of
particles – bosons and their superpartners – fermions. Considering this, it also implies that
boson natured gravitons have a gauge fermion superpartner with spin
Gravitino, which mediate supergravity interactions . Supersymmetric theories make
gravity arise in a natural way and in coming sections we focus on establishing its applica-
tion as a good component of DM.
2.1. Effective field theory (EFT)
This is another theory working under quantum gravity (QG) and it forms our base
for describing dark matter and gravitino relations. EFT accounts for gravity as a well-
defined series dependent on higher powers of R, the curvature of space time, as .
This is in contrast with Einstein’s series of gravity which is a linear function of R. We
consider higher orders in QG based on several parameters, mass of scalar field being
one with most consequences. Generally, values of ‘m’ are kept heavy so as to avoid the
effects of relativity breaking under plank length, but in a recent study Jose Cembranos
found out that making ‘m’ lighter automatically accounts for dark matter. The particle
introduced would be a gravitino with the ability to be casted as a scalar field that could
clump just like real matter . This is an especially elegant result as it does not require
us to introduce a new particle to the standard model and merely points towards a poten-
In another study conducted, this result was used to construct a model of our universe
that tracked its evolution through time, assuming gravity to be quantum in nature and
caused by gravitinos. The model showed hints of accelerated expansion at the exact point
of time we are in today and matched the rate very closely with present observational evi-
dence . This new perspective of thinking is advantageous to us, as it starts of with
general framework of gravity at quantum level rather the restricting itself to cosmological
contexts from the very start.
2.2. Gravitational Fields
The LIGO (Laser Interferometer Gravitational Waves Observatory) has already de-
tected many gravitational waves which are produced by all matter that accelerates. These
wave like ripples in space time travel at the speed of light and transport energy as gravi-
tational radiation. A gravitational field (gravitino field) is model used to explain the im-
pact of gravity on other objects and is observed in form of gravitational waves . It is
massless in nature and contains a spectrum of two massive fields of spin 2 and 0 whose
properties can be derived with help of quantum gravity . They have the ability to ide-
ally explain DM that is only gravitationally coupled to normal matter while postulating
its existence to be light in nature. The waves would also carry information about DM and
be directly related to its abundance.
2.3. Decay widths
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The intriguing property of such massless gravitational fields is that they decay both
gravitationally and to standard model particles . In this section, we shall attempt to
show a concise and brief version of the original derivation wherein the different decay
widths of these gravitino fields to various particles are calculated.
We start with general relativity and integrate the fluctuations due to gravitinos to get
the classical effective action at second order curvature.
Here R is Ricci scalar. Many complex summations of are included in later terms
which depend on the cosmological constant, which is the renormalization scale,
the Lagrangian and M as the total energy scale up to which we can trust the EFT. The
green’s function poles can be used to identify new degrees of freedom with respect to a
matrix. Two pairs of complex poles are found for each spin field which are then renormal-
ized till reduced plank scale. This allows us to obtain the gravitational decay width in
terms of mass of the field as:
Here is the reduced plank mass equal to and is the decay
width due to gravitation. Using this equation (Fig 2.) we can now calculate the decay
widths of these fields into various standard model particles. The result of such calcula-
tions is that the fields do not decay to gauge bosons and the charged leptons of the stand-
ard model, but they do decay to gluons such as photons and neutrinos with low enough
mass . Decay width to photons is given by:
The fact that gravitino fields decay to photons is especially emphasized as their ob-
servability during gamma ray bursts is of astronomical importance to us. The Unruh –
DeWitt detector implies a decay of gravitons into photons using this pathway :
The author will use the information provided until now to make the hypotheses that
follow below and these are subject to human error due to negligence/ignorance.
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Figure 2. The complete and general equation used to derive decay widths of gravitinos to standard model particles.
3. Approximate equivalence in Gamma Ray Flux
We illustrated in the above sections that gravity, when quantized as gravitino, could
account for dark matter and a field of such particles would decay into photons with a
considerable width. Using this result, it is also possible to calculate the flux of a gamma
ray produced upon decay of gravitinos. The in-depth calculations of the flux are shown
in this paper  for further reference but maybe be briefly summed up as:
where is the energy possessed by gamma rays that are produced by decay of dark
matter particle of mass . The flux of such a monochromatic gamma ray is given by
line of sight integral over dark matter distribution and the explicit component is:
where is the decay width and
is the milky way’s dark matter halo
density profile given by:
Using and we get local dark matter density of 0.4
The flux calculated now, assuming gravitons to have mass 200 GeV and lifetime
seconds is approximately in the range of units. This is also shown in
the graph (Fig 3.).
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Figure 3. This shows the predicted gamma ray flux from gravitino decay .
3.1. Methodology and Principle
It is known that neutron-neutron star collisions and black hole neutron star collisions
release huge gravitational waves which are detected by LIGO. The data observed from
gravitational waves publicly is available on the GW Open Science Center and after deep
query analysis of it using the fact that the theoretical mass range of neutron stars is gen-
erally between 1.174 – 2.116 solar masses, we list 5 GW events that have the possibility of
being emitted from neutron star mergers. The code used by the author during analysis is
listed in section 3.2 for reference.
A release of gamma ray burst should happen soon after a collision happens and this
is detected by observatories on earth usually within a short time interval of GW trigger
time. The public data on Heasarc NASA by the Fermi Gamma Ray Observatory is ana-
lyzed for listed 5 GW events to extract GRB trigger, time interval and fluence. Flux is then
calculated separately for each event using queried data. The time interval between GW
and GRB triggers is also mentioned for reader reference.
The author theorizes that since neutron star collisions release a huge number of grav-
itational waves and thus by implication gravitino fields in our model, some of these
gravitinos must have decayed into gamma rays. If energy/flux of these gamma rays is
calculated, suitable comparisons can be made between the computed value and the theo-
retical value of energy/flux hypothesized to be possessed by gamma rays after decay from
gravitino fields. Equal values must increase the probability that dark matter is indeed
made up of gravitinos for future conceptual investigations in this matter. Accordingly,
highly unequal values must also eliminate our idea to constitute DM with gravitinos.
The python code used by the author to query and analyze GW event catalogue is:
! pip install -q 'gwpy==2.0.2'
from gwosc.datasets import find_datasets
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from gwosc import datasets
print("List of available catalogs")
List of available catalogs
['GWTC-1-confident', 'GWTC-1-marginal', 'GWTC-2', 'GWTC-2.1-auxiliary', 'GWTC-2.1-confident',
'GWTC-2.1-marginal', 'GWTC-3-confident', 'GWTC-3-marginal', 'Initial_LIGO_Virgo', 'O1_O2-Pre-
liminary', 'O3_Discovery_Papers', 'O3_IMBH_marginal']
gwtc1 = datasets.find_datasets(type='events', catalog='all')
print('All events:', events)
print(datasets.find_datasets(type='events', catalog='any', detector="any", segment=(second-
from gwosc.datasets import event_secondarymass
result = event_secondarymass(1.174, 2.116)
print ('list of events:', result)
list of events: GW170817, GW190425, GW190917_114630, GW200105_162426,
Thus, GW170817, GW190425, GW190917 ,GW200105 and GW200115 are the events
which include a possible neutron star collision. The data for bursts observed on these
dates is extracted from HEARSEC and the fluence and time period is noted as shown in
Table 1. This shows the data for gamma ray bursts observed near given gravitational wave events.
GW event name
GRB event name
Trigger time gap
GRB fluence (erg/cm^2)
GRB time interval(sec)
Flux is calculated manually using the relation:
The plot of observed flux as function of energy for each event is shown along with the
straight line of predicted flux (Fig 4.).
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Figure 4. Flux values of GRBs from neutron star mergers plotted along with predicted value of flux
from gamma ray after gravitino decay
We infer from the plot graph that the flux of most events aligns approximately with the
theorized value. Minor time differences are noticed between GW triggers and GRB trig-
gers, implying the good possibility of both events originating from a common source.
The author attributes minor gaps between predicted and actual flux values to plausible
technological, source, numerical and human errors.
In this paper we have shown that the existence of dark matter is supported by ample
number of evidences and that its absence indeed causes serious issues to remain unex-
plained by our exclusive models. Its origin and composition are much contemplated
over by defining a quantum theory of gravity and the various implications it would
have. Gravitinos, the mediating particle of gravitational forces in supergravity, are
thought to constitute dark matter and in such a scenario, it is predicted that the gravita-
tional field would decay due to standard model particles. Its decay to photons would
eventually give rise to gamma rays with predicted values of flux. The author endeavors
to analyze gravitational wave and gamma ray bursts data from neutron star collisions in
order to obtain experimental flux observed. Both these values are clearly shown to be
approximately equal, implying that according to our model gravitinos must constitute
dark matter and have predictably decayed into gamma rays. Although there is a long
way to go before it can be said for certain what dark matter is composed of, this conclu-
sion helps us evaluate that the scope of quantum gravity. The result proceeds to further
cement our belief that gravitinos have a good candidacy to be considered as comprising
particles for dark matter.
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Funding: This research received no external funding or grants.
Data Availability Statement: The data used in this research for gravitational wave events has been
taken from https://www.gw-openscience.org/ and the coding interface used is https://colab.re-
ering%20Open%20Data.ipynb. The gamma ray burst data has been obtained from https://heas-
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