In non-attractor single-field inflation, one-loop corrections to superhorizon gravitational waves cancel, and a Ward identity explains why.
Spectrum of third-order tensor perturbations induced by excited scalar fields
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abstract
We calculate for the first time the third-order spectrum of gravitational waves sourced by the amplified scalar field perturbations during inflation using the in-in formalism, and discuss the conditions for the third-order spectrum to be smaller than the second-order one. Assuming an exponential growth of the sub-horizon modes of the scalar field perturbations, we find that the third-order spectrum increases faster than the second-order one as the amplification of the field perturbations increases, and thus the third-order spectrum dominates for detectable gravitational waves, which indicates that the perturbation theory breakdowns.
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One-loop corrections to infrared GWs is forbidden by symmetries
In non-attractor single-field inflation, one-loop corrections to superhorizon gravitational waves cancel, and a Ward identity explains why.