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

About

We use the in-in formalism to compute the non-Gaussian corrections to the energy density and anisotropies of gravitational waves induced 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 $\mathcal{R}$. We apply our formalism to an analytical model in which the ultra-slow-roll phase is followed by a constant-roll stage with a non-vanishing second slow-roll parameter $\eta$, and address the renormalization of the one-loop scalar power spectrum in this scenario..

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