Black hole formation and slow-roll inflation

TL;DR

This paper explores how certain inflation models can produce the necessary conditions for primordial black hole formation through specific spectral index running, providing new observational bounds and discussing broader scenarios.

Contribution

It introduces a new observational bound on the spectral index running in slow-roll inflation models and discusses black hole formation conditions in more general inflationary scenarios.

Findings

New bound n' < 0.026 on spectral index running

Conditions  << 1 and || << 1 are sufficient for spectrum derivation

Discussion of black hole production in broader inflation models

Abstract

Black hole formation may occur if the spectrum of the curvature perturbation \zeta increases strongly as the scale decreases. As no such increase is observed on cosmological scales, black hole formation requires strongly positive running n' of the spectral index n, though the running might only kick in below the `cosmological scales' probed by the CMB anisotropy and galaxy surveys. A concrete and well-motivated way of producing this running is through the running mass model of slow roll inflation. We obtain a new observational bound n' < 0.026 on the running provided by this model, improving an earlier result by a factor two. We also discuss black hole production in more general scenarios. We show that the usual conditions \epsilon << 1 and |\eta| << 1 are enough to derive the spectrum {\cal P}_{\zeta}(k), the introduction of higher order parameters \xi^{2} etc. being optional.