The signal of the stochastic gravitational wave background and the angular correlation of its energy density

TL;DR

This paper presents a new derivation of the angular dependence of the gravitational wave background's energy density, linking the measured signals to the universe's matter distribution in a clearer way.

Contribution

It introduces an independent derivation focusing on incoherent sources, clarifying the origin of angular correlations in the gravitational wave background.

Findings

Derivation of the angular dependence of the stochastic gravitational wave background.

Clarification of the relationship between measured signals and energy density.

Insight into the matter distribution's influence on gravitational wave anisotropies.

Abstract

The gravitational wave radiation emitted by all, resolved and unresolved, astrophysical sources in the observable universe generates a stochastic background. This background has a directional dependence inherited from the inhomogeneities of the matter distribution. This article proposes a new and independent derivation of the angular dependence of its energy density by focusing on the total gravitational wave signal produced by an ensemble of incoherent sources. This approach clarifies the origin of the angular correlation and the relation between the gravitational wave signal that can be measured by interferometers and the energy density of the stochastic background.