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

Abstract. Seery and Lidsey have calculated the three-point correlator of the light scalar fields, a few Hubble times after horizon exit during inflation. Lyth and Rodriguez have calculated the contribution of this correlator to the three-point correlator of the primordial curvature perturbation. We calculate an upper bound on that contribution, showing that it is too small ever to be observable.

Previous authors have calculated the mass function of primordial black holes only on scales which are well outside the horizon at the end of inflation. Here we extend the calculation to sub-horizon scales, on which the density perturbation never becomes classical. Regarding the formation of black holes as a 'measurement' of the (high peaks) of the density perturbation, we estimate a mass function by assuming that black holes form as soon as inflation ends, in those rare regions where the Bardeen potential exceeds a threshold value of Ψc ≃ 0.5.

We calculate the constraints on the primordial curvature perturbation at the end of inflation from the present day abundance of Primordial Black Holes (PBHs), as a function of the reheat temperature TRH. We first extend recent work on the formation of PBHs on scales which remain within the horizon during inflation and calculate the resulting constraints on the curvature perturbation. We then evaluate the constraint from PBHs that form, more conventionally, from super-horizon perturbations. The constraints apply for TRH < 10 8 GeV and the inclusion of sub-horizon PBHs leads to a limit which is roughly three times tighter than the bound from super-horizon PBHs.

We provide a detailed study of gravitational reheating in quintessential inflation generalizing previous analyses only available for the standard case when inflation is followed by an era dominated by the energy density of radiation. Quintessential inflation assumes a common origin for inflation and the dark energy of the Universe. In this scenario reheating can occur through gravitational particle production during the inflation-kination transition. We calculate numerically the amount of the radiation energy density, and determine the temperature T * at which radiation starts dominating over kination. The value of T * is controlled by the Hubble parameter H0 during inflation and the transition time ∆t, scaling as H 2 0 [ln(1/H0∆t)] 3/4 for H0∆t ≪ 1 and H 2 0 (H0∆t) −c for H0∆t ≫ 1. The model-dependent parameter c is found to be around 0.5 in two different parametrizations for the transition between inflation and kination.