No-go theorem for scalar-trispectrum-induced gravitational waves

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.

Automated summary

We demonstrate that the contribution of the primordial trispectrum to the scalar-induced stochastic gravitational wave background is limited in conventional inflationary scenarios. Scale-invariant theories with regular or local trispectrum shapes cannot significantly contribute due to their smallness compared to the relative one-loop correction of the scalar power spectrum. Additionally, a toy model for a scale-dependent scalar spectrum confirms the robustness of our no-go result.