Non-Gaussianities and the large $|\eta|$ approach to inflation

TL;DR

This paper analytically derives the bispectrum of curvature fluctuations in single field inflation, revealing complex scale and shape dependencies that influence primordial black hole formation and induced gravitational waves.

Contribution

It provides the first analytical calculation of the bispectrum at leading order in a $1/||$ expansion for scenarios producing primordial black holes.

Findings

Bispectrum exhibits rich scale and shape dependence.

Results show sensitivity of induced gravitational waves to the curvature bispectrum.

Analytical approach offers new insights into non-Gaussianities in inflation.

Abstract

The physics of primordial black holes can be affected by the non-Gaussian statistics of the density fluctuations that generate them. Therefore, it is important to have good theoretical control of the higher-order correlation functions for primordial curvature perturbations. By working at leading order in a $1/|\eta|$ expansion, we analytically determine the bispectrum of curvature fluctuations for single field inflationary scenarios producing primordial black holes. The bispectrum has a rich scale and shape dependence, and its features depend on the dynamics of the would-be decaying mode. We apply our analytical results to study gravitational waves induced at second order by enhanced curvature fluctuations. Their statistical properties are derived in terms of convolution integrals over wide momentum ranges, and they are sensitive on the scale and shape dependence of the curvature bispectrum we analytically computed.