Multifield inflation beyond $N_\mathrm{field}=2$: non-Gaussianities and single-field effective theory

TL;DR

This paper develops a comprehensive analytical framework for understanding the dynamics and non-Gaussianities of multiple scalar fields during inflation, extending single-field effective theories to multifield scenarios with complex geometries.

Contribution

It introduces a general formalism for linear and cubic perturbations in multifield inflation, including effects beyond simple field space curvature and the derivation of an effective single-field theory.

Findings

Rich geometrical effects in perturbation dynamics beyond scalar curvature.

Potential instabilities from entropic basis rotation when N_field ≥ 3.

Effective cubic action with predictions for bispectrum coefficients.

Abstract

In this article, we study in detail the linear dynamics and cubic interactions for any number $N_\mathrm{field}$ of scalar fields during inflation, directly in terms of the observable curvature perturbation $\zeta$ and $N_\mathrm{field}-1$ entropic fluctuations, a choice that is more suitable for analytical works. In the linear equations of motion for the perturbations, we uncover rich geometrical effects beyond terms involving just the scalar curvature of the field space, and that come from the non-canonical kinetic structure of the scalar fields when the dimension of the field space is larger than two. Moreover, we show that a fast rotation of the local entropic basis can result in negative eigenvalues for the entropic mass matrix, potentially destabilising the background dynamics when $N_\mathrm{field} \geqslant 3$. We also explain how to render manifest the sizes of cubic interactions between the adiabatic and the entropic fluctuations, extending a previous work of ours to any number of interacting fields. As a first analytical application of our generic formalism, we derive the effective single-field theory for perturbations up to cubic order when all entropic fluctuations are heavy enough to be integrated out. In a slow-varying limit, we recover the cubic action expected from the effective field theory of inflation, but with a prediction for the usual Wilson coefficients in terms of the multifield parameters, thus proposing a new interpretation of the bispectrum in this generic $N_\mathrm{field}$ context.