Large slow-roll corrections to the bispectrum of noncanonical inflation

TL;DR

This paper calculates advanced slow-roll corrections to the inflationary bispectrum for noncanonical models, providing precise estimates and identifying new detectable bispectrum shapes relevant for cosmological observations.

Contribution

It extends the calculation of the bispectrum to next-order slow-roll corrections in noncanonical inflation, including explicit formulas and new shape features.

Findings

Corrections can be several tens of percent in DBI inflation.

A new bispectrum shape similar to Galileon models is identified.

The results satisfy the next-order Maldacena consistency condition.

Abstract

Nongaussian statistics are a powerful discriminant between inflationary models, particularly those with noncanonical kinetic terms. Focusing on theories where the Lagrangian is an arbitrary Lorentz-invariant function of a scalar field and its first derivatives, we review and extend the calculation of the observable three-point function. We compute the "next-order" slow-roll corrections to the bispectrum in closed form, and obtain quantitative estimates of their magnitude in DBI and power-law k-inflation. In the DBI case our results enable us to estimate corrections from the shape of the potential and the warp factor: these can be of order several tens of percent. We track the possible sources of large logarithms which can spoil ordinary perturbation theory, and use them to obtain a general formula for the scale dependence of the bispectrum. Our result satisfies the next-order version of Maldacena's consistency condition and an equivalent consistency condition for the scale dependence. We identify a new bispectrum shape available at next-order, which is similar to a shape encountered in Galileon models. If fNL is sufficiently large this shape may be independently detectable.