Thermodynamics and kinetic theory of relativistic gases in 2D cosmological models

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 energymomentum 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.

Dilaton gravity in two dimensions

“…[247,197]. 44 Recently cosmological solutions in the JT model have been obtained [68,271]. 45 Here ref.…”

Transition from accelerated to decelerated regimes in JT and CGHS cosmologies

“…In this work, as a sequence to our previous effort [7], we want to discuss the existence of positive-acceleration solutions in 2D cosmologies; these related to the description of an inflation period and its transition to a decelerated period. We show that a consistent formulation is possible when the usual barotropic equation of state is replaced by the van der Waals equation (VDW), as was proposed by Capozziello et al [9] in 4D models and explored by one of these authors [10].…”

“…Another analysis of the JT model, in a cosmological context [4], considered the dilaton as a dynamical field. The best cosmological results obtained using the JT model include the description of a Universe filled with ordinary matter or/and electromagnetic radiation, where its behavior is described in terms of the temporal evolution of the scale parameter, the energy density and the total pressure [2,4,7]. A remarkable point here is that positive accelerated regimes (such as an inflationary Universe) were possible only under very special conditions, such as a negative vacuum energy density for the inflaton and violation of the weak energy condition for the matter/radiation constituents [2].…”

Irreversible processes and the accelerated-decelerated phases of the Universe

“…In Eckart (or firstorder) thermodynamic theory the non-equilibrium pressure is considered as a constitutive quantity which is proportional to the Hubble parameter and whose proportionality factor is the coefficient bulk viscosity (see e.g. the works [1][2][3]), whereas in extended (second-order or causal) thermodynamic theory the non-equilibrium pressure is supposed to obey an evolution equation (see e.g. the works [4][5][6][7][8][9][10][11][12]).…”