Loop Corrections in Gravitational Wave Spectrum in Single Field Inflation

Abstract: We study the one-loop corrections in power spectrum of long gravitational waves induced from small scale modes in the models of single field inflation undergoing a phase of ultra-slow-roll (USR). We show that the spectrum of long tensor perturbations are largely unaffected by the loop corrections from the short scalar modes. In particular, the spectrum of long tensor perturbations is insensitive to the sharpness of the transition from the USR phase to the final slow-roll phase. This is in contrast to the case of scalar power spectrum in which the loop corrections can be large for a sharp transition while it is slow-roll suppressed in a mild transition. We study the tensor-scalar-scalar bispectrum in the squeezed limit and demonstrate that the Maldacena consistency condition does hold.