Expansion history-dependent oscillations in the scalar-induced gravitational wave background

TL;DR

This paper studies how the expansion history after inflation influences oscillations in the gravitational wave background caused by small-scale features during inflation, revealing potential signals of non-standard post-inflationary physics.

Contribution

It provides a detailed analysis of how the post-inflationary expansion affects oscillatory features in the scalar-induced gravitational wave spectrum, including sharp and resonant features.

Findings

Resonant feature oscillations are unaffected by the equation of state, but their amplitudes are.

Oscillations are prominent only if the sound speed c_s<1.

A high amplitude oscillation (>20%) indicates non-standard post-inflationary expansion.

Abstract

Oscillations in the frequency profile of the scalar-induced contribution to the stochastic gravitational wave background are a characteristic signal for small-scale features during inflation. We investigate how this oscillatory frequency profile is affected by the expansion history of the post-inflationary universe. Our results are applicable as long as the equation of state of the universe can be taken as constant during the period in which the gravitational waves are produced, and we compute the spectrum of gravitational waves induced by both sharp and resonant features, associated with oscillations in $k$ and $\log(k)$, respectively. For resonant features, the frequencies of the oscillatory contributions to the gravitational wave spectrum are unaffected by the equation of state, but not their relative amplitudes, allowing one to extract information about both inflationary physics and the post-inflationary expansion history from the oscillatory pattern. For sharp features we find that the gravitational wave spectrum only exhibits prominent modulations as long as the propagation speed of density fluctuations is $c_s<1$, with a frequency larger by a factor $c_s^{-1}$ than that of the scalar power spectrum. We find that the stiffer the equation of state, the larger the relative amplitude of the oscillations. In particular, a relative amplitude significantly higher than $20 \%$ is not achievable for the 'standard' case of radiation domination, and would be a smoking-gun signal of both nontrivial inflationary dynamics on small scales, and a post-inflationary universe not dominated by radiation.