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Register a new userTheoretical foundations of the reduced relativistic gas in the cosmological perturbed context
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Added by
Gival Pordeus-da-Silva
Publication date
2019
fields
Physics
and research's language is
English
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The Reduced Relativistic Gas (RRG) is a simplified version of the ideal relativistic gas, which assumes that all particles have the same momentum magnitude. Although this is a very idealized situation, the resulting model preserves the phenomenology of Maxwell-Boltzmann distribution and, in some situations, can be described as a perfect fluid, without introducing large errors in both cosmological background and first-order perturbations. The perfect fluid description of RRG model was already used to study the warmness of dark matter, massive neutrinos and interaction of baryons and photons before recombination, showing very good agreement with previous works based on the full Einstein-Boltzmann system of equations. In order to understand these results and construct a more general and formal framework for RRG, we develop a theoretical description of first-order cosmological perturbations of RRG, based on a distribution function which encodes the simplifying assumption that all particles have the same momentum magnitude. The full set of Einstein-Boltzmann equations for RRG distribution are derived and quantities beyond the perfect fluid approximation are studied. Using RRG to describe warm dark matter, we show that, for particles with $m sim text{keV}$, the perfect fluid approximation is valid on scales $k < 10, text{h}/text{Mpc}$, for most of the universe evolution. We also determine initial conditions for RRG in the early universe and study the evolution of potential in a toy model of universe composed only by RRG.
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In this paper one examine analytical solutions for flat and non-flat universes composed by four components namely hot matter (ultra-relativistic), warm matter (relativistic), cold matter (non-relativistic) and cosmological constant. The warm matter is treated as a reduced relativistic gas and the other three components are treated in the usual way. The solutions achieved contains one, two or three components of which one component is of warm matter type. A solution involving all the four components was not found.
We use the framework of a recently proposed model of reduced relativistic gas (RRG) to obtain the bounds for $Omega$s of Dark Matter and Dark Energy (in the present case, a cosmological constant), taking into consideration an arbitrary warmness of Dark Matter. An equivalent equation of state has been used by Sakharov to predict the oscillations in the matter power spectrum. Two kind of tests are accounted for in what follows, namely the ones coming from the dynamics of the conformal factor of the homogeneous and isotropic metric and also the ones based on linear cosmic perturbations. The RRG model demonstrated its high effectiveness, permitting to explore a large volume in the space of mentioned parameters in a rather economic way. Taking together the results of such tests as Supernova type Ia (Union2 sample), $H(z)$, CMB ($R$ factor), BAO and LSS (2dfGRS data), we confirm that $La$CDM is the most favored model. At the same time, for the 2dfGRS data alone we found that an alternative model with a very small quantity of a Dark Matter is also viable. This output is potentially relevant in view of the fact that the LSS is the only test which can not be affected by the possible quantum contributions to the low-energy gravitational action.
We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-reduced density matrix. We show that equilibrium properties of a grand canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its one-reduced density matrix. We further prove the existence of a Kohn-Sham system capable of reproducing the one-reduced density matrix of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.
Reduced Relativistic Gas (RRG) is a useful approach to describe the warm dark matter (WDM) or the warmness of baryonic matter in the approximation when the interaction between the particles is irrelevant. The use of Maxwell distribution leads to the complicated equation of state of the J{u}ttner model of relativistic ideal gas. The RRG enables one to reproduce the same physical situation but in a much simpler form. For this reason RRG can be a useful tool for the theories with some sort of a new Physics. On the other hand, even without the qualitatively new physical implementations, the RRG can be useful to describe the general features of WDM in a model-independent way. In this sense one can see, in particular, to which extent the cosmological manifestations of WDM may be dependent on its Particle Physics background. In the present work RRG is used as a complementary approach to derive the main observational exponents for the WDM in a model-independent way. The only assumption concerns a non-negligible velocity $v$ for dark matter particles which is parameterized by the warmness parameter $b$. The relatively high values of $b$ ( $b^2gtrsim 10^{-6}$) erase the radiation (photons and neutrinos) dominated epoch and cause an early warm matter domination after inflation. Furthermore, RRG approach enables one to quantify the lack of power in linear matter spectrum at small scales and in particular, reproduces the relative transfer function commonly used in context of WDM with accuracy of $lesssim 1%$. A warmness with $b^2lesssim 10^{-6}$ (equivalent to $vlesssim 300 km/s$) does not alter significantly the CMB power spectrum and is in agreement with the background observational tests.
CO measurements of z~1-4 galaxies have found that their baryonic gas fractions are significantly higher than galaxies at z=0, with values ranging from 20-80 %. Here, we suggest that the gas fractions inferred from observations of star-forming galaxies at high-z are overestimated, owing to the adoption of locally-calibrated CO-H2 conversion factors (Xco). Evidence from both observations and numerical models suggest that Xco varies smoothly with the physical properties of galaxies, and that Xco can be parameterised simply as a function of both gas phase metallicity and observed CO surface brightness. When applying this functional form, we find fgas ~10-40 % in galaxies with M*=10^10-10^12 Msun at high-z. Moreover, the scatter in the observed fgas-M* relation is lowered by a factor of two. The lower inferred gas fractions arise physically because the interstellar media of high-z galaxies have higher velocity dispersions and gas temperatures than their local counterparts, which results in an Xco that is lower than the z=0 value for both quiescent discs and starbursts. We further compare these gas fractions to those predicted by cosmological galaxy formation models. We show that while the canonically inferred gas fractions from observations are a factor of 2-3 larger at a given stellar mass than predicted by models, our rederived Xco values for z=1-4 galaxies results in revised gas fractions that agree significantly better with the simulations.
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