Path integral for multi-field inflation

TL;DR

This paper develops a path integral approach for analyzing quantum cosmological perturbations in multi-field inflation, enabling detailed calculations of power spectra and non-Gaussianities.

Contribution

It introduces a gauge fixing method based on Poisson brackets and derives general expressions for power spectra and bispectra in multi-field inflation.

Findings

Derived the most general power spectrum including interactions.

Formulated convenient gauges suitable for multi-field inflation.

Discussed interaction contributions to the bispectrum.

Abstract

We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.