# On general features of warm dark matter with reduced relativistic gas

## TL;DR

This paper uses the Reduced Relativistic Gas model to analyze the general features of warm dark matter, providing a simplified, model-independent way to understand its cosmological effects and observational signatures.

## Contribution

It introduces the RRG approach as a tool to study WDM's features and effects without detailed particle physics assumptions, highlighting its utility in cosmological modeling.

## Key findings

- RRG reproduces the small-scale matter power spectrum with less than 1% error.
- High warmness parameter values erase the radiation-dominated epoch.
- Low warmness parameter values are consistent with CMB observations.

## Abstract

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 $b$ ( $b^2\gtrsim 10^{-6}$) 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 $b^2\lesssim 10^{-6}$ (equivalent to $v\lesssim 300 km/s$) does not alter significantly the CMB power spectrum and is in agreement with the background observational tests.