Momentum of cosmological acoustic field

TL;DR

This paper explores the acoustic spacetime in perturbed FLRW universes, revealing a simplified perturbation equation and conserved quantities related to spacetime symmetries, leading to a stable, spectrum-independent analysis of density perturbations.

Contribution

It introduces a canonical formalism in acoustic spacetime, simplifying perturbation equations and identifying conserved quantities linked to spacetime symmetries in cosmological models.

Findings

Perturbations obey a d'Alembert equation in acoustic spacetime.

Fourier coefficients of perturbations are time-independent.

Perturbation spectrum is invariant under hypersurface choice.

Abstract

The acoustic spacetime corresponding to perturbed Friedman-Lemaitre-Robertson-Walker universe inherit the space isometries from the original FLRW model, but essentially differs in dynamics. The scale factor manifestly depends on the equation of state of the matter content. Despite the higher complexity of the background evolution the perturbation equation in this space is substantially simpler: the density perturbations obey d'Alembert equation. Canonical formalism reconstructed in the acoustic spacetime enables one to employ the Klein-Gordon scalar product. Consequently, the Fourier decomposition of the perturbation field provide the time-independent Fourier coefficients and the time-independent spectrum. The perturbation spectrum does not depend of the choice of the Cauchy hypersurface from which the data are collected. Noether constants associated with the six-parameter isometry group define the components of the momentum, hyperbolic momentum and angular momentum of sound.