Acoustics of early universe. I. Flat versus open universe models

TL;DR

This paper introduces a gauge-invariant perturbation formalism to compare acoustic phenomena in flat and open universe models, revealing curvature effects on wave propagation and spectrum imprint.

Contribution

It presents a unified perturbation description applicable to all curvature signs and highlights how curvature influences acoustic wave dispersion and spectra in early universe models.

Findings

Density perturbations behave like waves in flat universe.

Curvature causes dispersion of sound in open universe.

A minimal frequency threshold exists in open universe for wave propagation.

Abstract

A simple perturbation description unique for all signs of curvature, and based on the gauge-invariant formalisms is proposed to demonstrate that: (1) The density perturbations propagate in the flat radiation-dominated universe in exactly the same way as electromagnetic or gravitational waves propagate in the epoch of the matter domination. (2) In the open universe, sounds are dispersed by curvature. The space curvature defines the minimal frequency $\omega_{\rm c}$ below which the propagation of perturbations is forbidden. Gaussian acoustic fields are considered and the curvature imprint in the perturbations spectrum is discussed.