Non-Gaussian perturbations in hybrid inflation

TL;DR

This paper develops a comprehensive second-order perturbation framework for two-field inflation and applies it to hybrid inflation with a waterfall field σ. By deriving a master equation for the second-order metric perturbation and the gauge-invariant curvature perturbation, the authors isolate the σ-dependent contributions and show that σ-induced non-Gaussianities can dominate over inflaton-induced ones when the σ mass satisfies $m_σ^2/H^2 \\gtrsim \epsilon,\eta$, potentially yielding observable signatures in the CMB bispectrum. The work highlights the importance of multi-field dynamics for primordial non-Gaussianity and introduces the non-Gaussianity kernel K as a momentum-dependent measure to connect theory with observations, with Planck offering meaningful constraints for favorable parameter ranges. Overall, the results provide a concrete, testable prediction for hybrid inflation and emphasize the role of the waterfall field in shaping early-universe statistics.

Abstract

We consider second order inflationary perturbations in the case of two scalar fields, $σ$ and the inflaton $φ$. We derive an expression for the non-Gaussianity of perturbations and apply the results to hybrid inflation. We isolate the contributions due to $σ$ and evaluate the resulting terms to show that $σ$-induced non-Gaussianities dominate over inflaton-induced non-Gaussianities when $m^2_σ \gtrsim ηH^2$, where $η$ is the slow-roll parameter. This may provide a useful test of hybrid inflation in forthcoming CMB experiments.