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

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_\zeta of the primordial curvature perturbation \zeta, 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_\zeta and the bispectrum B_\zeta. Sizeable values for f_{NL} arise even if \zeta is 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 \zeta series expansion, and its truncation, are valid. 2. we must apply the correct condition for the (possible) loop dominance in B_\zeta and/or P_\zeta. 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.Comment: 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 = 0, conclusions unchanged. Version accepted for publication in Journal of Cosmology and Astroparticle Physic

Non-Gaussian Inflationary Perturbations from the dS/CFT Correspondence

We use the dS/CFT correspondence and bulk gravity to predict the form of the renormalized holographic three-point correlation function of the operator which is dual to the inflaton field perturbation during single-field, slow-roll inflation. Using Maldcaena's formulation of the correspondence, this correlator can be related to the three-point function of the curvature perturbation generated during single-field inflation, and we find exact agreement with previous bulk QFT calculations. This provides a consistency check on existing derivations of the non-Gaussianity from single-field inflation and also yields insight into the nature of the dS/CFT correspondence. As a result of our calculation, we obtain the properly renormalized dS/CFT one-point function, including boundary contributions where derivative interactions are present in the bulk. In principle, our method may be employed to derive the n-point correlators of the inflationary curvature perturbation within the context of (n-1)th-order perturbation theory, rather than nth-order theory as in conventional approaches.Comment: 23 pages, uses iopart.cls. Replaced with version accepted by JCAP; some clarifications in the introduction, and references adde

Higher order contributions to the primordial non-Gaussianity

In this paper we calculate additional contributions to the part of the non-Gaussianity of the primordial curvature perturbation ζ that comes from the three-point correlator of the field perturbations. We estimate this contribution using the following models for the origin of ζ: single-component inflation, multicomponent chaotic inflation, a two-component 'hybrid' inflationary model and the curvaton scenario. In all of these models, the additional contributions to the primordial non-Gaussianity considered here are too small to ever be detected