Simple route to non-Gaussianity in inflation

Abstract

We present a simple way to calculate non-Gaussianity in inflation using fully non-linear equations on long wavelengths with stochastic sources to take into account the short-wavelength quantum fluctuations. Our formalism includes both scalar metric and matter perturbations, combining them into variables which are invariant under changes of time slicing in the long-wavelength limit. We illustrate this method with a perturbative calculation in the single-field slow-roll case. We also introduce a convenient choice of variables to graphically present the full momentum dependence of the three-point correlator.

Figures (1)

• Figure 1: (a) The three-point correlator (\ref{['3pcorr']}), (\ref{['three point']}) for single-field slow-roll inflation, multiplied by $k_1^3 k_2^3 k_3^3/((k_1^2+k_2^2+k_3^2)/2)^{3/2} [(\kappa^4/16)(H^4/{\tilde{\epsilon}}^2)(2{\tilde{\epsilon}}+{\tilde{\eta}})]^{-1}$, plotted to show its dependence on the relative size of the three momenta. (b) An explanation of the triangular domain used, defined in (\ref{['plotvars']}).