Non-Gaussian perturbations from multi-field inflation

TL;DR

The paper develops a gauge-invariant, second-order formalism to characterize primordial non-Gaussianity from inflation. It expresses the curvature perturbation via the perturbed expansion using the delta-N formalism and relates it to gauge-invariant field perturbations, deriving both the intrinsic field bispectrum and the local transformation contribution to the curvature bispectrum. In single-field slow-roll, it reproduces Maldacena’s results and the n-1 consistency relation; in multi-field scenarios it shows how cross-correlations and isocurvature modes modify or suppress non-Gaussianity, with local-type non-Gaussianity arising in isocurvature-dominated limits. The framework accommodates scale-dependent spectra and provides a unified description of non-Gaussianity across inflationary models, with implications for CMB and large-scale structure probes.

Abstract

We show how the primordial bispectrum of density perturbations from inflation may be characterised in terms of manifestly gauge-invariant cosmological perturbations at second order. The primordial metric perturbation, zeta, describing the perturbed expansion of uniform-density hypersurfaces on large scales is related to scalar field perturbations on unperturbed (spatially-flat) hypersurfaces at first- and second-order. The bispectrum of the metric perturbation is thus composed of (i) a local contribution due to the second-order gauge-transformation, and (ii) the instrinsic bispectrum of the field perturbations on spatially flat hypersurfaces. We generalise previous results to allow for scale-dependence of the scalar field power spectra and correlations that can develop between fields on super-Hubble scales.