Anisotropies of Gravitational Wave Backgrounds: A Line Of Sight Approach

TL;DR

This paper develops a line-of-sight formalism to calculate anisotropies in gravitational wave backgrounds, considering various cosmological effects, and provides expressions for their angular power spectrum.

Contribution

It introduces a novel geometric optics approach to quantify gravitational wave background anisotropies, including new analytical expressions for their angular power spectrum.

Findings

Derived expressions for anisotropy angular power spectrum.

Identified key cosmological sources of anisotropies.

Established analogy with CMB photon anisotropies.

Abstract

In the weak field regime, gravitational waves can be considered as being made up of collisionless, relativistic tensor modes that travel along null geodesics of the perturbed background metric. We work in this geometric optics picture to calculate the anisotropies in gravitational wave backgrounds resulting from astrophysical and cosmological sources. Our formalism yields expressions for the angular power spectrum of the anisotropies. We show how the anisotropies are sourced by intrinsic, Doppler, Sachs-Wolfe, and Integrated Sachs-Wolfe terms in analogy with Cosmic Microwave Background photons.