Group velocity of gravitational waves in an expanding universe

TL;DR

This paper investigates how gravitational waves propagate in an expanding universe, revealing that their group velocity can exceed the speed of light under certain conditions, leading to observable timing shifts.

Contribution

It provides a detailed analysis of gravitational wave group velocity in a cosmological setting, highlighting superluminal propagation effects during specific cosmic eras.

Findings

Group velocity exceeds light speed for certain wavelengths in an expanding universe.

Timing shifts of gravitational waves from distant black hole mergers are on the order of ten picoseconds.

Propagation effects could influence gravitational wave observations during matter/dark energy dominated eras.

Abstract

The group velocity of gravitational waves in a flat Friedman-Robertson-Walker universe is investigated. For plane waves with wavelength well inside the horizon, and a universe filled with an ideal fluid with the pressure to density ratio less than 1/3, the group velocity is greater than the velocity of light. As a result, a planar pulse of gravitational waves propagating through the universe during the matter/dark energy dominated era arrives to the observer with the peak shifted towards the forefront. For gravitational waves emitted by inspiralling supermassive black holes at the edge of the observable universe, the typical shift that remains after the effects of nonplanarity are suppressed is of order of ten picoseconds.