Local Scale-Dependent Non-Gaussian Curvature Perturbations at Cubic Order

TL;DR

This paper investigates the non-Gaussian features of curvature perturbations caused by cubic terms, analyzing loop corrections and their impact on non-linear parameters across different momentum scales.

Contribution

It introduces a method to compute three-loop order non-Gaussianities for general momenta and explores unique non-linear signals in the squeezed limit.

Findings

Loop corrections can change the sign of $f_{NL}^{sq.}$ with scale.

A momentum limit exists where $ au_{NL} < 0$ can occur.

The paper develops a procedure for evaluating complex loop integrals.

Abstract

We calculate non-Gaussianities in the bispectrum and trispectrum arising from the cubic term in the local expansion of the scalar curvature perturbation. We compute to three-loop order and for general momenta. A procedure for evaluating the leading behavior of the resulting loop-integrals is developed and discussed. Finally, we survey unique non-linear signals which could arise from the cubic term in the squeezed limit. In particular, it is shown that loop corrections can cause $f_{NL}^{sq.}$ to change sign as the momentum scale is varied. There also exists a momentum limit where $\tau_{NL} <0$ can be realized.