Gravitational waves generated by second order effects during inflation

TL;DR

This work analyzes gravitational waves produced by second-order effects during inflation, focusing on the non-linear coupling between scalar and tensor modes. It presents a detailed comparison between a covariant 1+3 perturbation framework and a metric-based Bardeen formalism, including a slow-roll inflation illustration. The authors derive and map the tensor perturbation dynamics in both formalisms, identify a local master variable for the covariant approach, and quantify the second-order GW power, showing it is subdominant on super-Hubble scales while highlighting a key non-Gaussian signature through the $f^{\mathcal{E},\mathcal{R}\mathcal{R}}_{NL}$ coupling relevant for CMB bispectra. The results clarify the relative strengths of the two formalisms and provide a pathway to constrain inflationary scenarios via non-Gaussianity and B-mode signatures in the CMB.

Abstract

The generation of gravitational waves during inflation due to the non-linear coupling of scalar and tensor modes is discussed. Two methods describing gravitational wave perturbations are used and compared: a covariant and local approach, as well as a metric-based analysis based on the Bardeen formalism. An application to slow-roll inflation is also described.