Primordial trispectrum from inflation

Abstract

We use the $\ensuremath{\delta}N$ formalism to describe the leading order contributions to the primordial power spectrum, bispectrum, and trispectrum in multiple-field models of inflation at leading order in a perturbative expansion. In slow-roll models where the initial field fluctuations at Hubble exit are nearly Gaussian, any detectable non-Gaussianity is expected to come from super-Hubble evolution. We show that the contribution to the primordial trispectrum can be described by two nonlinearity parameters, ${\ensuremath{\tau}}_{NL}$ and ${g}_{NL}$, which are dependent upon the second and third derivatives of the local expansion with respect to the field values during inflation.