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

TL;DR

The paper addresses how primordial black holes can form dark matter within a GW170817-compatible Horndeski framework by inducing a transient ultra-slow-roll phase through a kinetic G3 term, without altering the inflationary potential. The approach preserves standard CMB predictions while generating a sharp small-scale peak in the curvature power spectrum that yields asteroid-mass PBHs with abundances up to $f_{\rm PBH} \sim 0.9$ and implies potentially detectable scalar-induced gravitational waves. Key results show that an exponential X-dependence in $G_3$ localizes USR and creates a peak at $k_{\rm peak}\sim 10^{14}\ \mathrm{Mpc}^{-1}$, translating to PBHs of order $M_{\rm PBH}\sim 10^{-16} M_\odot$. The work highlights a robust mechanism with moderate tuning, linking early-universe modified gravity to the present dark matter content, and points to future probes via stochastic GWs and non-Gaussianity effects.

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.

Figures (4)

• Figure 1: Evolution of the field $\phi$ and the Hubble parameter $H$ with respect to the e-fold number $N$, for the case (a) of Table \ref{['tab:PBH_cases']}.
• Figure 2: Evolution of the first ($\epsilon$) and second ($\eta$) slow-roll parameters with respect to the e-fold number $N$, for the case (a) of Table \ref{['tab:PBH_cases']}.
• Figure 3: Profile of the scalar power spectrum $\mathcal{P}_{\zeta}$ as a function of the comoving wavenumber $k$, for the case (a) (red color) and (b) (green color) of Table \ref{['tab:PBH_cases']}.
• Figure 4: The PBHs abundance $f_{\text{PBH}}$ with respect to the PBHs masses $M$, on top of the observational contraints from CMB (pink color), GWs (greeen color), Microlensing (orange color), WD (purple color) and BH Evaporation (blue color) , for the case (a) and case (b) of Table \ref{['tab:PBH_cases']}. The asteroid-mass window, at roughly $10^{-11}-10^{-16} M_{\odot}$, could account for 100% of DM.