Probing non-Gaussianities with the high frequency tail of induced gravitational waves

TL;DR

This paper explores how the high frequency tail of induced gravitational waves can reveal non-Gaussian features of primordial fluctuations, providing a new way to probe early universe physics.

Contribution

It demonstrates that the spectral tilt of high frequency gravitational waves can infer the non-Gaussianity parameter $f_{NL}$ and discusses degeneracies with the universe's equation of state.

Findings

High frequency spectral tilt relates to $f_{NL}$.

Non-Gaussianity broadens the GW peak slightly.

Constraints on primordial spectrum parameters from GW and CMB data.

Abstract

We investigate in detail the spectrum of gravitational waves induced by a peaked primordial curvature power spectrum generated in single field inflationary models. We argue that the $f_{\rm NL}$ parameter can be inferred by measuring the high frequency spectral tilt of the induced gravitational waves. We also show that the intrinsically non-Gaussian impact of $f_{\rm NL}$ in $\Omega_{\rm GW}$ is to broaden its peak, although at a negligible level in order not to overproduce primordial black holes. We discuss possible degeneracies in the high frequency spectral tilt between $f_{\rm NL}$ and a general equation of state of the universe $w$. Finally, we discuss the constraints on the amplitude, peak and slope (or equivalently, $f_{\rm NL}$) of the primordial power spectrum by combining current and future gravitational wave experiments with limits on $\mu$ distortions from the cosmic microwave background.