Numerical evaluation of the bispectrum in multiple field inflation

TL;DR

This paper develops a comprehensive numerical framework for calculating the power spectrum and bispectrum in multi-field inflation models, capturing all relevant effects at tree-level and enabling precise predictions for upcoming galaxy surveys.

Contribution

It introduces a novel, complete numerical method for evaluating the bispectrum in multi-field inflation, including all key effects at tree-level without matching quantum and classical regimes.

Findings

Accurate bispectrum predictions for models with |fNL| of order unity or less.

Framework applicable to a wide range of multi-field inflation scenarios.

First quantitative predictions of bispectra for several example models.

Abstract

We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop expansion, including (i) interference between growing and decaying modes near horizon exit; (ii) correlation and coupling between species near horizon exit and on superhorizon scales; (iii) contributions from mass terms; and (iv) all contributions from coupling to gravity. We track the evolution of each correlation function from the vacuum state through horizon exit and the superhorizon regime, with no need to match quantum and classical parts of the calculation; when integrated, our approach corresponds exactly with the tree-level Schwinger or 'in-in' formulation of quantum field theory. In this paper we give the equations necessary to evolve all two- and three-point correlation functions together with suitable initial conditions. The final formalism is suitable to compute the amplitude, shape, and scale dependence of the bispectrum in models with |fNL| of order unity or less, which are a target for future galaxy surveys such as Euclid, DESI and LSST. As an illustration we apply our framework to a number of examples, obtaining quantitatively accurate predictions for their bispectra for the first time. Two accompanying reports describe publicly-available software packages that implement the method.