Review of local non-Gaussianity from multi-field inflation

TL;DR

The review addresses the problem of generating observable local non-Gaussianity in multi-field inflation, outlining mechanisms both after horizon exit (curvaton, modulated reheating, inhomogeneous end of inflation) and during inflation (slow-roll multi-field dynamics and non-slow-roll regimes). It employs the $\delta N$ formalism and a Hamilton–Jacobi–type approach to derive analytic and exact results for the curvature perturbation and non-Gaussian observables, including higher-order statistics like the trispectrum. The authors provide explicit conditions under which a large $f_{ m NL}$ can arise in separable potentials, present detailed two-field hybrid-inflation examples, and exhibit an exact non-slow-roll solution showing sizeable non-Gaussianity near the end of inflation. They also discuss the scale dependence of $f_{ m NL}$ and the relationship between the bispectrum and trispectrum parameters, highlighting observational prospects for Planck and large-scale structure as discriminants among competing multi-field models. The work thus offers a comprehensive framework for predicting and interpreting local non-Gaussian signals in multi-field inflation scenarios.

Abstract

We review models which generate a large non-Gaussianity of the local form. We first briefly consider three models which generate the non-Gaussianity either at or after the end of inflation; the curvaton scenario, modulated (p)reheating and an inhomogeneous end of inflation. We then focus on ways of generating the non-Gaussianity during inflation. We derive general conditions which a product or sum separable potential must satisfy in order to generate a large local bispectrum during slow-roll inflation. As an application we consider two-field hybrid inflation. We then derive a formalism not based on slow roll which can be applied to models in which the slow-roll parameters become large before inflation ends. An exactly soluble two-field model is given in which this happens. Finally we also consider further non-Gaussian observables; a scale dependence of f_NL and the trispectrum.

Figures (2)

• Figure 1: Plot showing $f_{NL}$ as a function of $\epsilon_H$ towards the end of inflation, for the values of the parameters given in the text. Inflation ends when $\epsilon_H=1$; for this example $f_{NL}\simeq59$ at that time.
• Figure 2: Left plot shows the trajectory considered for the parameters given after eq. (\ref{['fNLconcrete2']}) superimposed on a contour plot of the potential. The square on the trajectory indicates a point along the trajectory one $e$-folding before inflation ends as $\phi$ and $\chi$ roll towards zero. This shows that the fields roll much more quickly during the final stage of inflation, and the trajectory curves near the end. The right plot shows the potential for the same parameter values. Notice that inflation ends on the plateau long before the potential becomes negative.