Boosted perturbations at the end of inflation

Abstract

We study the effect on the primordial cosmological perturbations of a sharp transition from inflationary to a radiation and matter dominated epoch respectively. We assume that the perturbations are generated by the vacuum fluctuations of a scalar field slowly rolling down its potential, and that the transition into the subsequent epoch takes place much faster than a Hubble time. The behaviour of the superhorizon perturbations corresponding to cosmological scales in this case is well known. However, it is not clear how perturbations on scales of and smaller than the Hubble horizon scale at the end of inflation may evolve through such a transition. We derive the evolution equation for the gravitational potential Ψ, which allows us to study the evolution of the perturbations on all scales under these circumstances. We show that for a certain range of scales inside the horizon at the end of inflation, the amplitude of the perturbations are enhanced relative to the superhorizon scales. This enhancement may lead to the overproduction of Primordial Black Holes (PBHs), and therefore constrain the dynamics of the transitions that take place at the end of inflation.

Brane annihilations during inflation

“…As in standard hybrid inflation models [57,58] the hyper-surface of the first stack's collision, and thus the transition between the two phases, is set by a certain value of an inflaton field, φ 1 = φ c for us. Treating the transition as instantaneous, that is assuming ∆t ≪ H −1 (t c ), the cosmological matching conditions relating perturbations before and after the collision become [59][60][61] [Φ] ± = 0 ,…”

“…However, we do not know the exact stringy details of tachyon formation and the brane collisions, nor the mechanism of energy transfer into radiation, especially in a non-trivial background with background fluxes present and collisions between multiple branes and anti-braens, see for example [62,63]. Nevertheless, we expect that perturbations in φ 1 are predominantly carried over by perturbations in radiation so that we can use (59) and (60) in order to perform the matching. We still keep some effects of radiation via the change in the equation of state parameter w; by means of the Bogoliubov coefficients we can relate the solutions in the two slow-roll inflationary regimes by using the matching conditions (61).…”

Unification models with reheating via primordial black holes

“…Ref. [25], or indeed due to preheating [26]. Moreover, the relative growth of ρ PBH with respect to other components is largest for PBHs formed at t end .…”

Fields annihilation and particles creation in DBI inflation

“…More specifically, in models where the matching conditions are imposed on a comoving hyper-surface one requires that both the extrinsic and the intrinsic curvatures to be continuos across this hyper-surface. These result in the following matching conditions [57][58][59] [Φ]…”