The Huygens principle and cosmological gravitational waves in the Regge-Wheeler gauge

TL;DR

This paper investigates how axial gravitational waves propagate in Friedman universes, showing that their behavior depends on the era and wavelength, with short waves following the Huygens principle and long waves experiencing backscatter.

Contribution

It derives the evolution equation for axial gravitational waves in the Regge-Wheeler gauge within Friedman universes and analyzes their propagation characteristics across different cosmic eras.

Findings

Gravitational waves obey the Huygens principle in the radiation era.

Long waves can backscatter in the matter era.

Short waves approximately satisfy the Huygens principle.

Abstract

We study the propagation of axial gravitational waves in Friedman universes. The evolution equation is obtained in the Regge-Wheeler gauge. The gravitational waves obey the Huygens principle in the radiation dominated era, but in the matter dominated universe their propagation depends on their wavelengths, with the scale fixed essentially by the Hubble radius. Short waves practically satisfy the Huygens principle while long waves can backscatter off the curvature of a spacetime.