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-$\delta N$ 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.

matches published version in JCAP. 25 pages plus appendices (total 33 pages), 12 figures

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• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• Stochastic inflation with gradient interactions
• Non-Gaussianities and Primordial Black Holes
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• Eternal inflation near inflection points: a challenge to primordial black hole models
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting