Stochastic density fluctuations in the radiation era of the Universe

Abstract

The linear stochastic hydrodynamical equations of the radiation-matter-one-component fluid in the Universe before the recombination era are solved. The stochastic ‘forces’ in the heat flux and the viscous stress tensor are described according the procedure of Landau and Lifshitz. In the case of a low density universe, where the effects of the thermal conductivity can be neglected with respect to the shear viscosity, we find analytical solutions of the dispersion relation for the different modes and of the density correlation function$\overline {\rho _{1m} (k, t) \rho _{1m} ( - k, t)}$. At the very Jeans length, this density correlation function exhibits a linear (for very large times) or a cubic (for small times) time dependence instead of a frozen-in character of this special mode.