A Practical Theorem on Gravitational Wave Backgrounds

TL;DR

This paper presents a simple, cosmology-independent relationship linking the gravitational wave background spectrum to individual source energy spectra and remnant density, enabling easier computation and uncertainty assessment.

Contribution

It introduces a practical theorem that simplifies calculating gravitational wave backgrounds from various astrophysical sources without detailed cosmological modeling.

Findings

The background spectrum depends mainly on source energy and remnant density.

The relationship is largely independent of cosmological parameters.

It facilitates quick estimates of gravitational wave backgrounds.

Abstract

There is an extremely simple relationship between the spectrum of the gravitational wave background produced by a cosmological distribution of discrete gravitational wave sources, the total time-integrated energy spectrum of an individual source, and the present-day comoving number density of remnants. Stated in this way, the background is entirely independent of the cosmology, and only weakly dependent on the evolutionary history of the sources. This relationship allows one easily to compute the amplitude and spectrum of cosmic gravitational wave backgrounds from a broad range of astrophysical sources, and to evaluate the uncertainties therein.