Cosmological baryon sound waves coupled with the primeval radiation

The fluid equations for the baryon-electron system in an expanding universe are derived from the Boltzmann equation. The effect of the Compton interaction is taken into account properly in order to evaluate the photon-electron collisional term. As an application, the acoustic motions of the baryon-electron system after recombination are investigated. The effective adiabatic index γ is computed for sound waves of various wavelengths, assuming the perturbation amplitude is small. The oscillations are found to be dumped when γ changes from between 1 (for an isothermal process) to 5/3 (for an adiabatic process).