On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part I: the Bispectrum

Abstract

We show in this paper that it is possible to attain very high, {\it including observable}, values for the level of non-gaussianity f_{NL} associated with the bispectrum B_ζof the primordial curvature perturbation ζ, in a subclass of small-field {\it slow-roll} models of inflation with canonical kinetic terms. Such a result is obtained by taking care of loop corrections both in the spectrum P_ζand the bispectrum B_ζ. Sizeable values for f_{NL} arise even if ζis generated during inflation. Five issues are considered when constraining the available parameter space: 1. we must ensure that we are in a perturbative regime so that the ζseries expansion, and its truncation, are valid. 2. we must apply the correct condition for the (possible) loop dominance in B_ζand/or P_ζ. 3. we must satisfy the spectrum normalisation condition. 4. we must satisfy the spectral tilt constraint. 5. we must have enough inflation to solve the horizon problem.

LaTeX file, 40 pages, 6 figures, Main body: 26 pages, Appendix: 8 pages, References: 6 pages. v2: minor grammatical changes, references added and updated, a few changes reflecting the fact that <ζ> = 0, conclusions unchanged. Version accepted for publication in Journal of Cosmology and Astroparticle Physics