Primordial black hole dark matter from ultra-slow-roll inflation in Horndeski gravity

TL;DR

This paper demonstrates that ultra-slow-roll inflation within Horndeski gravity can produce asteroid-mass primordial black holes that could constitute most of dark matter, with distinctive gravitational-wave signals.

Contribution

It introduces a novel mechanism in Horndeski gravity where kinetic-dependent interactions induce ultra-slow-roll inflation, amplifying small-scale perturbations without potential features.

Findings

Primordial black holes of about 10^{-16} solar masses can form and account for up to 90% of dark matter.

The model predicts sharp peaks in the scalar power spectrum.

Potential observable gravitational-wave signatures from scalar-induced gravitational waves.

Abstract

Primordial black holes (PBHs) provide a well-motivated non-particle candidate for dark matter, requiring an enhancement of curvature perturbations on small inflationary scales consistent with observational constraints. In this work we study PBH production within Horndeski gravity, accounting for compatibility with the GW170817 constraint on the gravitational-wave speed and imposing a constant coupling to the Ricci scalar. Under these conditions, and assuming an inflaton field characterised by a canonical kinetic term and a smooth potential, the inflationary dynamics is controlled by the cubic Horndeski interaction. We show that a suitable kinetic dependence of the latter enhances the effective friction acting on the inflaton, inducing a transient ultra-slow-roll phase embedded in an otherwise standard slow-roll evolution. Interestingly, this mechanism amplifies the curvature power spectrum on small scales without introducing any feature in the potential. For representative parameter choices we find that pronounced peaks in the scalar power spectrum are generated, leading to the formation of asteroid-mass PBHs with masses of order $\mathcal{O}(10^{-16})\,M_\odot$, which can account for a substantial fraction of the dark matter abundance, reaching $f_{\rm PBH}\simeq 0.9$, while satisfying current observational constraints. The resulting sharp features in the scalar power spectrum also imply potentially observable scalar-induced gravitational-wave signatures.