Theory of relativistic hydrodynamic fluctuations before H-recombination

Using a previously developed relativistic extension of the Landau-Lifshitz theory of hydrodynamic fluctuations, the spectrum of energy density fluctuations before hydrogen recombination is calculated both for the radiation-dominated and the matter-dominated cases. The spectrum consists of a high frequency adiabatic and a low frequency isobar part. The isobar part is proportional to the inverse proton number density multiplied by the squared ratio of the rest energy density and the radiation energy density in the radiation dominated era. In the matter dominated era it is proportional to the inverse proton number density.The adiabatic part is proportional to the inverse photon number density in both cases. In the spectrum of temperature fluctuations the adiabatic part is the dominating one.The general part of the analysis is performed within a gauge invariant formalism.