The evolution of nonlinear hydrodynamical density fluctuations of the photon-plasma gas during the recombination era of the Universe

On the basis of the hydrodynamical equations of a two-component gas (photons and hydrogen with coupling via Thomson scattering) in the recombination era of the Universe (standard model), the evolution of the density perturbations up to second order are calculated. It is shown, that the generated second-order amplitudes of the density fluctuations of the matter reach values of the same order as the first-order amplitudes within only one tenth of the expansion time for fluctuations with wavelengths corresponding to 10⁷ M . Upper limits in the density fluctuations (for the gravitationally instable modes) up to which first-order calculations are valid, are given. This calculation indicates that the linear perturbation analysis is very restricted, especially at wavelengths near the lower limit of the Jeans length.The linear analysis would be a good approximation only for density fluctuations of the matter with the density contrast less than 10^–5–10^–4 at the recombination era. Therefore, a nonlinear analysis which is not based on a perturbation series is required for studying the evolution of the density perturbations, because for this we need a density contrast of 10^–2–10^–3 at the end of the recombination era.