Non-Gaussianity from the second-order cosmological perturbation -: art. no. 123508

Several conserved and/or gauge-invariant quantities described as the second-order curvature perturbation have been given in the literature. We revisit various scenarios for the generation of second-order non-Gaussianity in the primordial curvature perturbation zeta, employing for the first time a unified notation and focusing on the normalization f(NL) of the bispectrum. When zeta first appears a few Hubble times after horizon exit, vertical bar f(NL)vertical bar is much less than 1 and is, therefore, negligible. Thereafter zeta ( and hence fNL) is conserved as long as the pressure is a unique function of energy density ( adiabatic pressure). Nonadiabatic pressure comes presumably only from the effect of fields, other than the one pointing along the inflationary trajectory, which are light during inflation ("light noninflaton fields''). During single-component inflation fNL is constant, but multicomponent inflation might generate vertical bar f(NL)vertical bar similar to 1 or bigger. Preheating can affect fNL only in atypical scenarios where it involves light noninflaton fields. The simplest curvaton scenario typically gives f(NL) << -1 or f(NL) = + 5/4. The inhomogeneous reheating scenario can give a wide range of values for f(NL). Unless there is a detection, observation can eventually provide a limit vertical bar f(NL)vertical bar less than or similar to 1, at which level it will be crucial to calculate the precise observational limit using second-order theory.