Gravitational waves in Friedman-Lemaitre-Robertson-Walker cosmology, material perturbations and cosmological rotation, and the Huygens principle

TL;DR

This paper investigates how gravitational waves propagate in cosmological models, showing their effects on matter and the conditions under which the Huygens principle holds or breaks down.

Contribution

It demonstrates that polar gravitational waves perturb matter density and velocity components, and establishes the conditions for the validity of the Huygens principle in different cosmological scenarios.

Findings

Polar waves perturb density and velocity components.

Axial waves induce local cosmological rotation.

Huygens principle holds in radiation spacetimes without cosmological constant.

Abstract

We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the Friedman-Lemaitre-Robertson-Walker spacetimes. Axial gravitational waves can influence only the azimuthal velocity, leading to local cosmological rotation. The whole gravitational dynamics reduces to the single "master equation" that has the same form for polar and axial modes. That allows us to conclude that the status of the Huygens principle is the same for axial and polar gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.