δNversus covariant perturbative approach to non-Gaussianity outside the horizon in multifield inflation

Abstract

We compute the super-Hubble evolution of non-Gaussianity of primordial curvature perturbations in two-field inflation models by employing two formalisms: $\ensuremath{\delta}N$ and covariant formalisms. Although the two formalisms treat the evolution of fluctuations radically different, we show that the formulas of the ${f}_{\mathrm{NL}}$ parameter agree quantitatively with each other within 1% accuracy. We analytically find that the amplitude of ${f}_{\mathrm{NL}}$ decays no faster than ${a}^{\ensuremath{-}3}$ as the inflationary trajectory reaches to the adiabatic limit for generic potentials.