Bispectrum at NLO in single field inflation: conservation and squeezed limit

TL;DR

This paper investigates the bispectrum at NLO in single field inflation, confirming the conservation and consistency relations near the squeezed limit despite infrared divergences.

Contribution

It provides an independent validation of bispectrum conservation and consistency relations in single field inflation at NLO, even with infrared divergences present.

Findings

Bispectrum conservation holds near the squeezed limit.

Consistency relation between bispectrum and power spectrum remains valid.

Infrared divergences do not invalidate key inflationary relations.

Abstract

In a recent paper, we computed the bispectrum of primordial density perturbations in CMB to second order in the slow-roll parameters of single field inflation, and found logarithmic infrared contributions that diverge in both large physical distances and squeezed limit where one momentum vanishes. In this work, we provide an independent test of the result by checking its conservation and the validity of the consistency relation between the squeezed limit of the bispectrum and the square of the power spectrum. Despite the violation of the main assumption for its general proofs which is the finiteness of the relevant observables in these limits, we find that the identity continues to hold in the vicinity of the squeezed limit and large time.