Loop Corrections in Bispectrum in USR Inflation with PBHs Formation

TL;DR

This paper computes one-loop corrections to the bispectrum in ultra-slow-roll inflation models relevant for primordial black holes, revealing potential observational constraints due to loop effects.

Contribution

It introduces a detailed calculation of loop corrections in the bispectrum within USR inflation, highlighting their impact on non-Gaussianity constraints for PBH formation models.

Findings

Loop corrections have local shape with $f_{NL}$ depending on USR phase duration.

Sharp transitions can cause loop corrections to violate observational bounds.

The formalism links bispectrum corrections to power spectrum features in USR inflation.

Abstract

We calculate the one-loop corrections in bispectrum of CMB scale perturbations induced from the small scale modes undergoing an intermediate phase of USR inflation in scenarios employed for PBHs formation. Using the formalism of effective field theory of inflation we calculate the cubic and quartic Hamiltonians and perform the in-in analysis for a subset of Feynman diagrams comprising both the cubic and the quartic exchange vertices. We show the one-loop corrections in bispectrum has the local shape with $f_{NL}$ having the same structure as the one-loop correction in power spectrum in their dependence on the duration of the USR phase and the sharpness of the transition to the final attractor phase. It is shown that in the models with a sharp transition the induced loop corrections in bispectrum can quickly violate the observational bounds on $f_{NL}$.