Perturbations of ionization fractions at the cosmological recombination epoch

Abstract

A development of perturbations of number densities of ions and electrons during recombination epoch is analysed. The equations for relative perturbations of ionization fractions were derived from the system of equations for accurate computation of the ionization history of the early Universe given by Seager et al. (1999,2000). It is shown that strong dependence of ionization and recombination rates on the density and temperature of plasma provides the significant deviations of amplitudes of ionization fractions relative perturbations from ones of baryon matter density adiabatic perturbations. Such deviations are most prominent for cosmological adiabatic perturbations of scales larger than sound horizon at recombination epoch. The amplitudes of relative perturbations of number densities of electrons and protons at last scattering surface exceed by factor of $\simeq$5 the amplitude of relative perturbation of baryons total number density, for helium ions this ratio reaches the value of $\simeq$18. For subhorizon cosmological perturbations these ratios appear to be essentially lesser and depend on oscillation phase at the moment of decoupling. These perturbations of number densities of ions and electrons at recombination epoch do not contribute to the intrinsic plasma temperature fluctuations but cause the ''corrugation'' of last scattering surface in optical depth, $\delta z_{dec}/(z_{dec}+1)\approx -\delta_b/3$, at scales larger than sound horizon. It may result into noticeable changes of precalculated values of CMB polarization pattern at several degrees angular scales.