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

a r X i v : g r - q c / 9 9 0 7 0 1 0 v 1 4 J u l 1 9 9 9 Exact inhomogeneous cosmologies whose source is a radiation-matter mixture with consistent thermodynamics. Roberto A. Sussman? and Diego Pavo?n? ? Instituto de Ciencias Nucleares UNAM, Apartado Postal 70-543, Me?xico DF, 04510, Me?xico. ? Departamento de F??sica, Facultad de Ciencias, Universidad Auto?noma de Barcelona, E- 08193 Bellaterra, Espan?a. 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 Lema??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. The fulfilment of (a), (b) and (c) restricts initial conditions in terms of an initial value function, ? (s) i , 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 ? (s) i 6= 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 (106K T 103K). Constraints on the observed anisotropy of the microwave cosmic radiation and the condition that decoupling occurs at T = T D ≈ 4 × 103 K yield an estimated value: |? (s) i | ≈ 10 ?8 which can be associated with a bo