Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D Cosmological Models

TL;DR

This paper develops a kinetic theory for relativistic gases in 2D cosmological models, deriving equilibrium and non-equilibrium properties, and analyzing their effects on universe evolution, including a maximum scale factor and a big crunch scenario.

Contribution

It introduces a 2D relativistic gas kinetic framework and solves the gravitational field equations considering non-equilibrium effects, revealing unique cosmological behaviors.

Findings

Cosmic scale factor reaches a maximum then decreases to a big crunch.

Existence of a false vacuum solution in 2D cosmology.

Pressure, energy density, and entropy evolve over time.

Abstract

A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat capacities in equilibrium. Furthermore, by using the method of Chapman and Enskog for a kinetic model of the Boltzmann equation the non-equilibrium energy-momentum tensor and the entropy production rate are determined for a universe described by a two-dimensional Robertson-Walker metric. The solutions of the gravitational field equations that consider the non-equilibrium energy-momentum tensor - associated with the coefficient of bulk viscosity - show that opposed to the four-dimensional case, the cosmic scale factor attains a maximum value at a finite time decreasing to a "big crunch" and that there exists a solution of the gravitational field equations corresponding to a "false vacuum". The evolution of the fields of pressure, energy density and entropy production rate with the time is also discussed.