Integrated Sachs-Wolfe Effect for Gravitational Radiation

TL;DR

This paper derives the gravitational wave equivalent of the Sachs-Wolfe effect, showing how large-scale structures influence wave properties and could reveal cosmic inhomogeneities and dark energy through measurable signals.

Contribution

It introduces the gravitational wave Sachs-Wolfe effect, extending the analogy from cosmic microwave background photons to gravitational waves in a perturbed universe.

Findings

Integrated effects can alter gravitational wave frequency, phase, and amplitude.

Potential to detect inhomogeneities and dark energy via gravitational wave observations.

Effects are significant for supermassive black hole binary signals.

Abstract

Gravitational waves are messengers carrying valuable information about their sources. For sources at cosmological distances, the waves will contain also the imprint left by the intervening matter. The situation is in close analogy with cosmic microwave photons, for which the large-scale structures the photons traverse contribute to the observed temperature anisotropies, in a process known as the integrated Sachs-Wolfe effect. We derive the gravitational wave counterpart of this effect for waves propagating on a Friedman-Robertson-Walker background with scalar perturbations. We find that the phase, frequency and amplitude of the gravitational waves experience Sachs-Wolfe type integrated effects, this in addition to the magnification effects on the amplitude from gravitational lensing. We show that for supermassive black hole binaries, the integrated effects could account for measurable changes on the frequency, chirp mass and luminosity distance of the binary, thus unveiling the presence of inhomogeneities, and potentially dark energy, in the Universe.