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

TL;DR

The work investigates the squeezed-limit behavior of the bispectrum at next-to-leading order in slow-roll for single-field inflation, where infrared logarithms introduce divergences both at large distances and in the squeezed limit. By analyzing the conservation of the bispectrum and verifying the Maldacena-style consistency relation at NLO, the authors show that the relation between the squeezed-limit bispectrum and the power spectrum survives these divergences in the late-time regime. They demonstrate that the naive $f_{NL}$ is time-dependent at NLO, and propose a conserved version $\hat f_{NL}$ which remains constant up to NLO and removes the squeezed-limit divergence. The results provide a nontrivial cross-check of the NLO bispectrum and reinforce the robustness of single-field inflation predictions under infrared effects, with implications for interpreting CMB non-Gaussianity measurements.

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.