Exact Solution to Standard Model Hydrodynamic Cosmological Perturbation Theory and its Implications for Acoustic Oscillations

Abstract

We present an exact solution to standard model cosmological perturbation theory in a matter-dominated, adiabatic, hydrodynamic era. The solution is in the form of hypergeometric functions. While such functions can oscillate with the sound velocity, they can only do so at high frequency. There is thus a maximum wavelength to these oscillations, with this maximum wavelength serving to provide a horizon for acoustic oscillations.