Spectral distortions of the microwave background radiation resulting from the damping of pressure waves

Initial inhomogeneities of the energy density of the primeval radiation field which enter the horizon prior to recombination lead to the formation of pressure waves as they enter the horizon. On scales less than about 5 × 10¹⁶ M_⊙ these waves will be damped prior to recombination by the processes of nonlinear dissipation and photon diffusion. The damping of these waves leaves its signature in spectral distortions of the microwave background radiation. The type of distortion depends upon the epoch of the damping. The magnitude of the distortion may be related to the amplitude of the waves which have been damped during a particular epoch. The amplitude of the perturbations of the energy density of the radiation field on a given scale may be related to those of the mass distribution on the same scale, in a manner which depends on whether the perturbations are of the isocurvature or adiabatic type. The limit on the amplitude of the initial perturbations of the mass distribution on the damping scale is used in conjunction with that on a much larger scale: the amplitude of the initial perturbations of the mass distribution needed to account for the observed variance of the number counts of galaxies at the current epoch, which depends on cosmological parameters. Combining these, an upper bound to the index of the initial power spectrum of the mass distribution is obtained. This bound depends on cosmological parameters, and on whether the initial perturbations are of the isocurvature or adiabatic type. The current and projected limits of the magnitude of the Compton y-parameter and of a chemical potential are used to constrain the index of the initial power spectrum of the mass distribution for several cosmological parameter sets for isocurvature and adiabatic perturbations.