Large slow-roll corrections to the bispectrum of noncanonical inflation

TL;DR

This work develops a comprehensive, closed-form calculation of next-order slow-roll corrections to the bispectrum for general single-field inflation with a noncanonical kinetic term, described by $P(X,\phi)$. Using the in-in formalism and a careful treatment of the third-order action, boundary terms, and propagator corrections, the authors quantify how these corrections modify $f_{\mathrm{NL}}$ and reveal rich scale- and shape-dependence, including new bispectrum shapes. In DBI and $k$-inflation, subleading corrections can be substantial (tens of percent) and depend on the potential and warp-factor shapes, with notable cancellations that can temper the overall size. The analysis confirms Maldacena’s consistency at next order and identifies an orthogonal, Galileon-like shape that could become observable with sufficient data, underscoring the need for precise templates and potentially guiding future observational strategies for Planck-like and next-generation CMB missions. Overall, the paper strengthens the link between microphysical Lagrangians and their non-Gaussian fingerprints, providing a rigorous framework to test noncanonical inflationary scenarios against high-precision cosmological data.

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.