# Anisotropy of the astrophysical gravitational wave background: analytic expression of the angular power spectrum and correlation with cosmological observations

## TL;DR

This paper derives an analytic expression for the anisotropies in the astrophysical gravitational wave background, linking it to cosmological observations and providing insights into its angular power spectrum and variance.

## Contribution

It presents a general expression for gravitational wave energy density applicable to any spacetime and specializes it to perturbed Friedmann-Lemaître spacetime to analyze anisotropies.

## Key findings

- Derived the angular power spectrum of the gravitational wave background.
- Established correlations between gravitational wave anisotropies and cosmological probes.
- Provided an expression for the variance of the gravitational wave background.

## Abstract

Unresolved and resolved sources of gravitational waves are at the origin of a stochastic gravitational wave background. While the computation of its mean density as a function of frequency in a homogeneous and isotropic universe is standard lore, the computation of its anisotropies requires to understand the coarse graining from local systems, to galactic scales and then to cosmology. An expression of the gravitational wave energy density valid in any general spacetime is derived. It is then specialized to a perturbed Friedmann-Lema\^itre spacetime in order to determine the angular power spectrum of this stochastic background as well as its correlation with other cosmological probes, such as the galaxy number counts and weak lensing. Our result for the angular power spectrum also provides an expression for the variance of the gravitational wave background.