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

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 $\delta \varphi$ 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.

arXiv comment34 pages, 4 figures. Figures corrected and discussion improved. Version accepted for publication in JCAP

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• Fundamental Physics and Cosmology with TianQin
• Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background
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