Exact inhomogeneous cosmologies whose source is a radiation-matter mixture with consistent thermodynamics

TL;DR

This paper presents a new class of exact inhomogeneous cosmological solutions modeling the radiative era with a viscous fluid, consistent thermodynamics, and initial conditions constrained by cosmic microwave background anisotropy.

Contribution

It introduces a physically plausible inhomogeneous cosmological model with a viscous fluid source, consistent thermodynamics, and initial conditions linked to primordial entropy fluctuations.

Findings

Estimated initial entropy fluctuation bound: |4_i^{(s)}|  10^{-8}

Decoupling temperature T_D  4  10^3 K

Jeans mass at decoupling  10^{16} M_\u00b7

Abstract

We derive a new class of exact solutions of Einstein's equations providing a physically plausible hydrodynamical description of cosmological matter in the radiative era ($10^6 K > T > 10^3 K$), between nucleosynthesis and decoupling. The solutions are characterized by the Lema\^{\i}tre-Tolman -Bondi metric with a viscous fluid source, subjected to the following conditions: (a) the equilibrium state variables satisfy the equation of state of a mixture of an ultra-relativistic and a non-relativistic ideal gases, where the internal energy of the latter has been neglected, (b) the particle numbers of the mixture components are independently conserved, (c) the viscous stress is consistent with the transport equation and entropy balance law of Extended Irreversible Thermodynamics, with the coefficient of shear viscosity provided by Kinetic Theory for the `radiative gas' model. The fulfilment of (a), (b) and (c) restricts initial conditions in terms of an initial value function, $\Delta_i^{(s)}$, related to the average of spatial gradients of the fluctuations of photon entropy per baryon in the initial hypersurface. Constraints on the observed anisotropy of the microwave cosmic radiation and the condition that decoupling occurs at $T=T_{_D}\approx 4\times 10^3$ K yield an estimated value: $|\Delta_i^{(s)}|\approx 10^{-8}$ which can be associated with a bound on promordial entropy fluctuations. The Jeans mass at decoupling is of the same order of magnitude as that of baryon dominated perturbation models ($\approx 10^{16} M_\odot$)