The acoustic wave equation in the expanding universe. Sachs-Wolfe theorem

TL;DR

This paper derives the acoustic wave equation in an expanding universe with arbitrary curvature, utilizing symbolic computation to analyze the Sachs-Wolfe theorem in cosmology.

Contribution

It presents a novel reduction of the acoustic field equations to the d'Alembert form in a static spacetime for arbitrary curvature.

Findings

Unified framework for acoustic wave propagation in curved spacetime

Application of symbolic computation to cosmological wave equations

Insights into Sachs-Wolfe effect in early universe

Abstract

In this paper the acoustic field propagating in the early hot ($p=\epsilon/$) universe of arbitrary space curvature ($K=0, \pm 1$) is considered. The field equations are reduced to the d'Alembert equation in an auxiliary static Roberson-Walker space-time. Symbolic computation in {\em Mathematica} is applied.