Exact inhomogeneous cosmologies whose source is a radiation-matter mixturewith consistent thermodynamics - art. no. 104023

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, between nucleosynthesis and decoupling. The solutions a re characterized by the Lemaitre-Tolman-Bondi metric with a viscous fluid s ource, subjected to the following conditions: (a) the equilibrium state var iables satisfy the equation of state of a mixture of an ultrarelativistic a nd a nonrelativistic ideal gases, where the internal energy of the latter h as been neglected, (b) the particle numbers of the mixture components are i ndependently conserved, (c) the viscous stress is consistent with the trans port equation and entropy balance law of extended irreversible thermodynami cs, with the coefficient of shear viscosity provided by kinetic theory. The satisfaction of (a), (b), and (c) restricts initial conditions in terms of an initial value function Delta(i)((s)), which in the limit of small densi ty contrasts becomes the average of spatial gradients of the fluctuations o f photon entropy per baryon in the initial hypersurface. For Delta(i)((s))n ot equal 0 and choosing the phenomenological coefficients of the "radiative gas" model, we have an interactive photon-baryon mixture under local therm al equilibrium, with radiation dominance and temperatures characteristic of the radiative era (10(6) K>T>10(3) K). Constraints on the observed anisotr opy of the microwave cosmic radiation and the condition that decoupling occ urs at T = T(D)approximate to 4 x 10(3) K yield an estimated value \Delta(i )((s))\approximate to 10(-8) which can be associated with a bound on promor dial entropy fluctuations. The Jeans mass at decoupling is of the same orde r of magnitude as that of baryon dominated perturbation models (approximate to 10(16)M(.)). [S0556-2821(99)07818-2].