Quantitative bispectra from multifield inflation

TL;DR

This paper develops a quantitative, non-slow-roll framework to compute the bispectrum in multifield inflation using a nonlinear long-wavelength formalism. By introducing a gradient variable $zeta_i^m$ and an orthonormal field-space basis, the authors reduce the evolution to a $2n-1$ system and derive an exact integral expression for the bispectrum in terms of horizon-crossing linear solutions and background parameters. The main result is an exact connected bispectrum on superhorizon scales, computed without slow-roll, and demonstrated numerically in a two-field quadratic model where non-Gaussianity briefly becomes large during a field-space turn but typically decays once isocurvature converts to adiabatic modes. This framework enables precise computation of non-Gaussianity for realistic multifield inflation models and informs observational prospects for CMB and large-scale structure, especially in scenarios where isocurvature modes play a transient yet impactful role.

Abstract

After simplifying and improving the non-Gaussian formalism we developed in previous work, we derive a quantitative expression for the three-point correlator (bispectrum) of the curvature perturbation in general multiple-field inflation models. Our result describes the evolution of non-Gaussianity on superhorizon scales caused by the nonlinear influence of isocurvature perturbations on the adiabatic perturbation during inflation. We then study a simple quadratic two-field potential and find that when slow roll breaks down and the field trajectory changes direction in field space, the non-Gaussianity can become large. However, for the simple models studied to date, the magnitude of this non-Gaussianity decays away after the isocurvature mode is converted into the adiabatic mode.

Figures (1)

• Figure 1: The non-Gaussianity parameter ${\tilde{f}}_\mathrm{NL}$ (\ref{['fNLdef']}) for the two momentum configurations described in the text together with the slow-roll parameters $-\eta^\parallel$ and $\eta^\perp$, plotted as a function of time in the model (\ref{['quadratic']}) with initial conditions $\phi_1=\phi_2=13\kappa^{-1}$ and mass ratio $m_2/m_1=12$.