No-go Theorem for Scalar-Trispectrum-Induced Gravitational Waves

TL;DR

This paper proves that in standard inflationary models, the primordial trispectrum cannot significantly enhance the scalar-induced gravitational wave background beyond the contribution from the scalar power spectrum, establishing a fundamental limit.

Contribution

It provides a rigorous no-go theorem showing the trispectrum's limited impact on gravitational waves in conventional inflationary scenarios.

Findings

Trispectrum contributions are always smaller than the scalar power spectrum correction.

The no-go theorem applies to both equilateral and local trispectrum shapes.

A toy model confirms the robustness of the no-go result for scale-dependent spectra.

Abstract

We show that the contribution of the primordial trispectrum to the energy density of the scalar-induced stochastic gravitational wave background cannot exceed the one from the scalar power spectrum in conventional inflationary scenarios. Specifically, we prove in the context of scale-invariant theories that neither regular trispectrum shapes peaking in so-called equilateral configurations, nor local trispectrum shapes diverging in soft momentum limits, can contribute significantly. Indeed, those contributions are always bound to be smaller than an order-one (or smaller) number multiplying the relative one-loop correction to the scalar power spectrum, necessarily much smaller than unity in order for the theory to be under perturbative control. Since a no-go theorem is only worth its assumptions, we also briefly discuss a toy model for a scale-dependent scalar spectrum, which confirms the robustness of our no-go result.