Probing the Nature of Dark Matter in the Universe
Author
Sarkar, Abir
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The dark matter is the most dominating matter candidate and a key driving force for the structure
formation in the universe. Despite decadelong searches, the precise nature and particle
properties of dark matter are still unknown. The standard cold dark matter candidate, the
Weakly Interacting Massive Particle(WIMP) can successfully describe the largescale features
of the universe. However, when it comes to the scales comparable to a galaxy or a group
of galaxies, it fails to explain the observations. The nature of the smallscale anomalies suggests
a lower amount of dark matter at the scales of interest and can be tackled with different
strategies. The simulation suites, used to produce the smallscale universe theoretically, can be
equipped with varieties of baryonic phenomena, leading to a better agreement with observation.
Another way is to use some new dark matter candidate altogether that reduces the smallscale
power. Many such alternative dark matter candidates have been suggested and explored in the
literature. The aim of the work presented in this thesis is to study the effects of smallscale
power reduction due to new dark matter physics on different cosmological observables.
In Chapter 2 of this thesis, we have discussed the particle physics properties of three dark
matter candidates proposed as alternatives of the WIMP. The rst one is the Late Forming
Dark Matter(LFDM), where dark matter is created due to a phase transition in the massless
neutrino sector [1] long after the Big Bang Nucleosynthesis(BBN). Another candidate is the
Ultra Light Axion Dark Matter(ULADM), which is born due to spontaneous symmetry breaking
in the early universe and is stuck to its initial condition because of the Hubble drag. When
the mass of the particle exceed the Hubble parameter, it decouples from the drag and starts
behaving like dark matter [2], with a freestreaming length that is dependent on its mass. The
last candidate we consider is the Charged Decaying Dark Matter (CHDM), which is born in iv
the radiation dominated era, after an instantaneous decay of a massive charged particle [3].
All of these dark matter candidates suppress smallscale power, though because of different
physical reasons. In the next three chapters, we have studied their e ects on various cosmological
observables. The methods of study, along with the data used to validate the theoretical
predictions and results are discussed below.
Chapter 3:
This chapter is based on the work performed in [4]. In this chapter, we focus on the LFDM
and study its e ects on linear matter power spectra at both small and large scales.
Method of Study: The LFDM model is speci ed by two parameters: The effective
massless neutrino degrees of freedom(DOF) Ne and the redshift of formation zf . We have
generated a set of matter power spectra using publicly available code CAMB for different sets of
Ne and zf , and performed a 2 analysis using matter power spectrum data to constrain the
model parameters. We have also considered a scenario, where a fraction flfdm of the total dark
matter is LFDM and repeated the exercise. We have computed multiparameter contours and
posterior probabilities by marginalization over redundant parameters that allow us to estimate
the model parameters.
The Data: The two parameterszf and Ne  affect the linear power spectrum at different
scales. The main impact of changing Ne is to alter the MRE epoch, shifting the peak of
the matter power spectrum, which is located at k ' 0:01hMpc1 in the standard model of
cosmology. We use the SDSS DR7 data [5] for our analysis. As the SDSS data on the galaxy
power spectrum gives the power at scales: k=0:02{0:1 h=Mpc, this data is sensitive to the
variation of Ne . On the other hand, the main effect of formation redshift zf is to suppress
the power at scales k > 0:1 h=Mpc. In this scales, we use the linear matter power spectrum,
reconstructed from Lyman forest power spectrum in the range: 0:2 < k < 4:8 h=Mpc from
[6,7]. We use 45 bandpowers from the SDSS galaxy data and 12 points from the reconstructed
linear power spectrum from the Lyman data.
Results: Our results can be summarized as follows. If all the presently observed CDM
is late forming, then both the data sets lead to upper limits on the redshift of formation of
LFDM, with Lyman data resulting in tighter bounds: zf < 3 106 at 99% con dence limit.
On the other hand, if we allow only a fraction of the CDM to form at late times, then we
improve the quality of t as compared to the standard CDM model for the Lyman data.
This is suggestive that the present data allows for a fraction 30% of the CDM to form at
zf ' 105. Therefore, our result underlines the importance of the Lyman data for studying
the smallscale power spectrum in alternative dark matter regime.
Chapter 4:
This chapter is based on the work performed in [8]. Here, we have studied the e ects of
smallscale power suppression on the Epoch of Reionization(EoR) and the evolution of collapsed
fraction of gas at high redshift. We have considered two of the alternative dark matter
candidates discussed in Chapter2 in this chapter: the LFDM and the ULADM.
Method of Study: Our method of constructing the reionization fi elds consists of three
steps: (i) Generating the dark matter distribution at the desired redshift, (ii) Identifying the
location and mass of collapsed dark matter halos within the simulation box, (iii) Generating
the neutral hydrogen map using an excursion set formalism. The assumption here is that the
hydrogen exactly traces the dark matter eld and the dark matter halos host the ionizing
sources. Given the uncertainty of reionization history, we do not assume a particular model
for reionization history xHI (z), where xHI is the fraction of neutral hydrogen in the universe.
Instead, we xed the redshift at z = 8 and the ionization fraction at xHI = 0:5 and compared
these models. We have produced Hi power spectra, and photon brightness temperature
fluctuation( Tb) maps to compare the alternative models with the standard CDM model. We
discard the models where no halo is formed to host the ionizing sources, or an absurdly high
number of ionizing photon is necessary to make xHI = 0:5 at z = 8 successfully.
The collapsed fraction, defined as the fraction of collapsed mass in haloes with masses larger
than a threshold mass M at a redshift z, is sensitive to the mass function of the haloes. As
obtaining the mass function from Nbody simulation is numerically expensive, we integrate
the ShethTormen mass function above the density threshold of collapse at a given redshift
for computing the collapsed fraction in case of LFDM models. For computing the collapsed
fraction for ULADM models, we integrate the halo mass functions derived by [9]. The collapsed
fractions are calculated for two threshold halo masses, 1010M and 5 1010M in the redshift
range 2 < z < 5 and compared to observational data. Models that are unable to produce the
observed collapsed fractions at high redshifts are discarded.
The Data: From absorption studies of the Damped Lyman (DLA) clouds, the evolution
of average mass density of Hi in the universe can be inferred. Assuming that the collapsed
fraction of baryons traces dark matter, this allows us to get an approximate measure of the
minimum amount of collapsed fraction of the total matter in the redshift range 2 < z < 5. We
have used the data of density of gas trapped in DLAs (HI ), at the mentioned redshift range
from [10, 11] and converted them to collapsed fraction of gas. The reconstructed collapsed
fractions are used to compare the theoretical predictions.
Results: Our method predicts an `insideout' reionization where the highdensity regions
are ionized rst. We fi nd that the Hi power for LFDM and ULADM models is greater than
the CDM model over a large range of scales 0:1 < k < 4Mpc1. In the maps of Tb, there
are two main differences between CDM and alternative models. The size of the ionized regions
is larger in the LFDM (ULADM) models and the Hi elds have stronger density contrast.
Checking the facts that halos are actually formed to host stars and a realistic number of ionizing
photons are produced to achieve the desired level of ionization, we put a rough limit on
zf 4 105 and ma ' 2:6 1023 eV as lower cuto s. Comparing the estimated collapsed
fraction with data we found weaker constraints on zf . 2 105 and ma . 1023 eV. All these
constraints are in good agreement with previous constraints.
Chapter 5:
This chapter is based on the work performed in [12]. The observable of interest here is the
spectral distortion in the Cosmic Microwave Background(CMB).
Method of Study: The distortion on the CMB spectra can occur due to heating or cooling
of the medium owing to several mechanisms at di erent times in the history of the universe. In
this work, we consider heating due to the dissipation of acoustic waves, wellknown as the Silk
Damping. The fraction of energy injected into the photon bath is a function of the evolution
of the fluctuation in gravitational potential and the CMB dipole 1. We have computed
the evolution of and 1 for all the three dark matter candidates studied in Chapter 2, along
with the WDM, using the publicly available code CMBFAST and axionCAMB. Using them, we
estimate the evolution of the heating rate and integrate it to get the distortion parameters.
The distortion parameters thus found are used to calculate the distorted CMB spectrum. The
nal output is the percentage change of the distortion parameters for the alternative dark
matter models with respect to the CDM model.
Results: The two earlier spectral distortions, namely the  and the idistortion, are not
found to be affected due to new dark matter physics. The ydistortion is the only one that carries
the signatures of smallscale power suppression. We conclude that, unless the constraints
on the model parameters found in previous studies are violated, the change in the ydistortion
parameter is not more than 14% compared to the standard model with identical spectral
shapes. ydistortion occurring from later phenomena, i.e., structure formation and tSZ e ects
in the galaxy clusters have orders of magnitude higher distortion parameters than the Silk
Damping, again with the same spectral shape. Thus, unless these foregrounds are understood
and cleared correctly, distinguishing between dark matter candidates which reduce smallscale
power is next to impossible.
Finally, our study shows that changing matter power at small scales can have noticeable
impacts on other observables of the universe. However, to see the difference, the phenomena
themselves are to be understood properly. The constraints found on the models using different
probes are in good agreement with each other. In future, we will extend our research by
investigating whether it is possible to accommodate an O(10 eV) particle as a dominating cold
dark matter candidate, by exploring its effects on linear matter power spectrum and CMB
spectral distortion.
Collections
 Physics (PHY) [316]
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