Teoria e aplicações do gás relativístico reduzido na cosmologia

Abstract

The Reduced Relativistic Gas (RRG) is a simplified version of the ideal relativistic gas, where it is assumed that all particles have the same momentum magnitude. Although this is a very idealized situation, the resulting model preserves the phenomenology of the Maxwell-Boltzmann distribution and, in some situations, can be described as a perfect fluid, without introducing large errors. 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. From this function, we derive the full set of Einstein-Boltzmann equations for RRG and study quantities beyond the perfect fluid approximation. We derive an analytical expression that relates the parameter of warmness to the mass of the particle and we also explicitly verify that the non-relativistic and ultra-relativistic limits are recovered. Furthermore, using RRG to describe warm dark matter (WDM), we show that for particles with m ∼ keV, the perfect fluid approximation is valid on scales with k < 10 h/Mpc, for most of the universe evolution. We also determined the initial conditions for RRG in the early universe and studied the evolution of the potential in a toy model composed only by RRG. Finally, we study in a semi-analytical way the sub-horizon evolution of the density contrast of the WDM in a model with WDM, radiation, and Λ, where the WDM is described by the RRG.