Universal infrared scaling of gravitational wave background spectra

TL;DR

This paper demonstrates a universal infrared scaling law for the gravitational wave background spectrum, showing it generally follows a cubic dependence on wave number under broad conditions.

Contribution

It establishes the universal $k^3$ infrared scaling of gravitational wave spectra for a wide class of sources satisfying specific physical conditions.

Findings

$ ext{Omega}_{ ext{GW}} ext{propto} k^3$ for many source types

The $k^3$ scaling holds when sources are bounded and active during radiation domination

Violations of conditions can lead to different spectral behaviors

Abstract

We study the general infrared behavior of the power spectrum of a stochastic gravitational wave background produced by stress tensor in the form bilinear in certain dynamical degrees of freedom. We find $\Omega_{\text{GW}}\propto k^3$ for a very wide class of the sources which satisfy a set of reasonable conditions. Namely, the $k^3$ scaling is universally valid when the source term is bounded in both frequency and time, is effective in a radiation-dominated stage, and for $k$ smaller than all the physical scales associated with the source, like the peak frequency, peak width, and time duration, etc. We also discuss possible violations of these conditions and their physical implications.