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

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, between nucleosynthesis and decoupling. The solutions are characterized by the Lemaitre-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 ultrarelativistic and a nonrelativistic 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. 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 density contrasts becomes the average of spatial gradients of the fluctuations of photon entropy per baryon in the initial hypersurface. For Delta(i)((s))not equal 0 and choosing the phenomenological coefficients of the "radiative gas" model, we have an interactive photon-baryon mixture under local thermal equilibrium, with radiation dominance and temperatures characteristic of the radiative era (10(6) K>T>10(3) K). Constraints on the observed anisotropy of the microwave cosmic radiation and the condition that decoupling occurs 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 promordial entropy fluctuations. The Jeans mass at decoupling is of the same order of magnitude as that of baryon dominated perturbation models (approximate to 10(16)M(.)). [S0556-2821(99)07818-2].