On the squeezed limit of the bispectrum in general single field inflation

TL;DR

This paper derives a general integral formula for the squeezed limit of the bispectrum in single field inflation models, verifying the consistency relation across various models and approximations.

Contribution

It provides a unified, approximation-free integral expression for the bispectrum in the squeezed limit, extending previous results to general single field inflation models.

Findings

Verifies the consistency relation in models with non-trivial sound speed.

Confirms the relation at first order in slow-varying approximation.

Extends verification to second order in canonical single field inflation.

Abstract

We investigate the consistency relation relating the squeezed limit of the bispectrum to the scalar spectral index in single field models of inflation. We give a simple integral formula for the bispectrum in the squeezed limit in terms of the free mode mode functions of the primordial curvature perturbation, in any Lorentz invariant single field model of inflation and without resorting to any approximation, generalizing a recent result obtained by Ganc and Komatsu in the case of canonical kinetic terms. We use our result to verify the consistency relation in an exactly solvable class of models with a non-trivial speed of sound. We then verify the consistency relation at the first non-trivial order in the slow-varying approximation in general single field inflation (a known result) and at second order in this approximation in canonical single field inflation.