Exact Lemaitre-Tolman-Bondi solutions for matter-radiation decoupling

Abstract

A new class of solutions of Einstein's equations is derived providing a physically plausible hydrodynamic description of cosmological matter in the radiation era of the Universe expansion. The solutions are characterized by the LTB metric with dissipative fluid sources, subjected to the following conditions: (i) tthe nonequilibrium state variables satisfy the equations of state of a mixture of relativistic and non-relativistic ideal gases, where the internal energy of the latter has been neglected, (ii) the particle numbers of the mixture components are independently conserved, (iii) the viscous stress is consistent with the transport equation and entropy balance law of extended irreversible thermodynamics with the coefficients of shear viscosity provided by kinetic theory. The Jeans mass at decoupling is of the same order of magnitude as that of baryons dominated models.