Gravitational waves in ultra-slow-roll and their anisotropy at two loops

TL;DR

This paper calculates two-loop non-Gaussian corrections to gravitational wave energy density and anisotropies during the radiation era after ultra-slow-roll inflation, revealing the dominant sources of non-Gaussianity and addressing renormalization issues.

Contribution

It introduces a diagrammatic approach with Feynman rules for two-loop calculations of gravitational wave non-Gaussianities post-ultra-slow-roll inflation, including a specific analytical model.

Findings

Intrinsic non-Gaussianity dominates over nonlinear relation effects.

The formalism applies to models with subsequent constant-roll stages.

Addresses renormalization of the scalar power spectrum in the scenario.

Abstract

We compute the non-Gaussian corrections to the energy density and anisotropies of gravitational waves induced during the radiation era after an ultra-slow-roll phase of inflation by using a diagrammatic approach, and present the corresponding Feynman rules. Our two-loop calculation includes both the intrinsic non-Gaussianity of the inflaton perturbation $\delta\phi$ and the non-Gaussianity arising from the nonlinear relation between the latter and the curvature perturbation $\mathcal{R}$, which we find to be subdominant with respect to the former. We apply our formalism to an analytical model in which the ultra-slow-roll phase is followed by a constant-roll stage with a nonvanishing second slow-roll parameter $\eta$, and address the renormalization of the one-loop scalar power spectrum in this scenario.