Uphill inflation

Abstract

Primordial black holes (PBH) may form from large cosmological perturbations, produced during inflation when the inflaton's velocity is sufficiently slowed down. This usually requires very flat regions in the inflationary potential. In this paper we investigate another possibility, namely that the inflaton climbs up its potential. When it turns back, its velocity crosses zero, which triggers a short phase of “uphill inflation” during which cosmological perturbations grow at a very fast rate. This naturally occurs in double-well potentials if the width of the well is close to the Planck scale. We include the effect of quantum diffusion in this scenario, which plays a crucial role, by means of the stochastic-δN formalism. We find that ultra-light black holes are produced with very high abundances, which do not depend on the energy scale at which uphill inflation occurs, and which suffer from substantially less fine tuning than in alternative PBH-production models. They are such that PBHs later drive a phase of PBH domination.

An exact model for enhancing/suppressing primordial fluctuations

“…It would also be interesting to repeat the analysis in the case when the slope in the second phase changes signs and eventually the system reaches ϕ ,N = 0 before rolling backward, as in ref. [63]. This case has been shown to abundantly produce tiny PBHs [63].…”

“…[63]. This case has been shown to abundantly produce tiny PBHs [63]. We note that the analysis of this paper might not be straightforwardly applicable to this case since the scalar field spends most of the time in non-attractor trajectories, as it must first reach ϕ ,N = 0 before approaching the attractor solution.…”

“…While this may lead to an interesting situation like that of ref. [63], we leave the case when λ 2 < 0 for future work. We also show in appendix A that in order to explain CMB observations [2], one needs JCAP03(2024)002 λ ∼ 0.18.…”

Primordial black holes and inflation from double-well potentials

“…The recent paper [54] discusses a setup similar to ours, concentrating on the crossing of the local maximum of a double-well potential which is associated with PBH formation but not the CMB. The authors go beyond our linear analysis by using stochastic inflation allowing them to study non-Gaussianities and their effect on PBH formation.…”

“…Regarding PBH production from double-well potentials, there have been a handful of proposals in the literature over the last three decades [51][52][53][54]. In these papers, the considered potentials were of the Coleman-Weinberg or Higgs-like nature.…”