The inflationary bispectrum with curved field-space

TL;DR

This paper develops a covariant framework to compute the inflationary bispectrum considering curved field-space, revealing how field-space curvature can significantly influence non-Gaussianity during inflation.

Contribution

It introduces a covariant method for calculating the bispectrum with arbitrary field-space metrics, including curvature effects, and extends the delta-N formalism to this setting.

Findings

Field-space curvature induces significant non-Gaussianities.

The framework accommodates non-minimal coupling models.

A practical toolkit for bispectrum computation in curved field-space.

Abstract

We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or "delta-N" expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.