A universal scaling law for gravitational waves induced during inflation

TL;DR

This paper derives a universal, simple formula for the spectral index of gravitational waves induced during inflation, applicable to various source fields and nearly scale-invariant spectra.

Contribution

It introduces a minimal-assumption, universal scaling law for the tensor spectral index of inflation-induced gravitational waves, simplifying analysis across models.

Findings

The spectral index is given by a simple, widely applicable formula.

Scale invariance persists regardless of the source spectrum.

The approach reproduces known results and aids future model estimations.

Abstract

We consider the stochastic gravitational wave background induced by arbitrary source fields that are amplified during cosmological inflation. The associated tensor spectral index is shown to be given, under minimal assumptions, by a simple formula easy to apply in most situations of accelerated expansion. For slow-roll inflation, the induced spectrum is nearly scale invariant, with an index deviating from the standard outcome of vacuum generated gravitational waves. Remarkably, we demonstrate that scale invariance remains true regardless of the original spectrum of the source. We show how this generic approach reproduces the literature on specific models of gravitational wave primordial sources, and discuss its limitations. It provides a very practical estimation of the tensor spectral index for future models, to which subleading corrections can then be added.