paper

Non-gaussianity from the second-order cosmological perturbation

arXiv:astro-ph/0502578 · doi:10.1103/PhysRevD.71.123508

Abstract

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 ζ, employing for the first time a unified notation and focusing on the normalisation f_{NL} of the bispectrum. When the classical curvature perturbation first appears a few Hubble times after horizon exit, |f_{NL}| is much less than 1 and is, therefore, negligible. Thereafter ζ(and hence f_{NL}) is conserved as long as the pressure is a unique function of energy density (adiabatic pressure). Non-adiabatic pressure comes presumably only from the effect of fields, other than the one pointing along the inflationary trajectory, which are light during inflation (`light non-inflaton fields'). During single-component inflation f_{NL} is constant, but multi-component inflation might generate |f_{NL}| \sim 1 or bigger. Preheating can affect f_{NL} only in atypical scenarios where it involves light non-inflaton fields. The curvaton scenario typically gives f_{NL} \ll -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 |f_{NL}| \lsim 1, at which level it will be crucial to calculate the precise observational limit using second order theory.

Latex file in Revtex style. 13 pages, 1 figure. v2: minor changes. Discussion in Subsection VI-A enlarged. References added. Conclusions unchanged. v3: minor typographic changes. Correlated and uncorrelated χ^2 non-gaussianity concepts and consequences introduced. Section VI-A enlarged. Small change in Table I. References updated and added. Conclusions unchanged. Version to appear in Physical Review D

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