Adiabatic models of the cosmological radiative era

Abstract

We consider a generalization of the Lemaitre-Tolman-Bondi (LTB) solutions by keeping the LTB metric but replacing its dust matter source by an imperfect fluid with anisotropic pressure $\Pi_{ab} $. Assuming that total matter-energy density $\rho$ is the sum of a rest mass term, $\rhom$, plus a radiation $\rhor=3p$ density where $p$ is the isotropic pressure, Einstein's equations are fully integrated without having to place any previous assumption on the form of $\Pi_{ab} $. Three particular cases of interest are contained: the usual LTB dust solutions (the dust limit), a class of FLRW cosmologies (the homogeneous limit) and of the Vaydia solution (the vacuum limit). Initial conditions are provided in terms of suitable averages and contrast functions of the initial densities of $\rhom, \rhor$ and the 3-dimensional Ricci scalar along an arbitrary initial surface $t=t_i$. We consider the source of the models as an interactive radiation-matter mixture in local thermal equilibrium that must be consistent with causal Extended Irreversible Thermodynamics (hence $\Pi_{ab} $ is shear viscosity). Assuming near equilibrium conditions associated with small initial density and curvature contrasts, the evolution of the models is qualitatively similar to that of adiabatic perturbations on a matter plus radiation FLRW background. We show that initial conditions exist that lead to thermodynamically consistent models, but only for the full transport equation of Extended Irreversible Thermodynamics. These interactive mixtures provide a reasonable approximation to a dissipative 'tight coupling' characteristic of radiation-matter mixtures in the radiative pre-decoupling era.