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

TL;DR

This paper provides an exact hypergeometric function solution to cosmological perturbation theory during a matter-dominated era, revealing a maximum wavelength for acoustic oscillations that acts as a horizon.

Contribution

It offers a novel exact analytical solution to standard model cosmological perturbations, highlighting a fundamental limit on acoustic oscillation wavelengths.

Findings

Identifies a maximum wavelength for acoustic oscillations.

Provides an exact hypergeometric function solution.

Suggests a horizon 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.