Non-gaussianity from the inflationary trispectrum

TL;DR

This work derives the first complete tree-level estimate of the trispectrum non-Gaussianity parameter $\tau_{\mathrm{NL}}$ for multi-field, uncoupled inflation using the $\delta N$ formalism, valid throughout slow-roll and including superhorizon evolution. It provides an exact analytic expression for $\tau_{\mathrm{NL}}$ in terms of slow-roll parameters and end-of-inflation isocurvature contributions, and specializes to the horizon-crossing approximation for monomial potentials relevant to Nflation. In the equal-power case, $\tau_{\mathrm{NL}}$ becomes independent of initial conditions and couplings, but remains suppressed by the tensor-to-scalar ratio $r$, making it observationally elusive for upcoming CMB experiments. The results establish a framework to compare inflationary scenarios and highlight that detectable trispectrum signals would point to alternative mechanisms such as curvaton models.

Abstract

We present an estimate for the non-linear parameter τ_NL, which measures the non-gaussianity imprinted in the trispectrum of the comoving curvature perturbation, ζ. Our estimate is valid throughout the inflationary era, until the slow-roll approximation breaks down, and takes into account the evolution of perturbations on superhorizon scales. We find that the non-gaussianity is always small if the field values at the end of inflation are negligible when compared to their values at horizon crossing. Under the same assumption, we show that in Nflation-type scenarios, where the potential is a sum of monomials, the non-gaussianity measured by τ_NL is independent of the couplings and initial conditions.