Inflationary Primordial Black Holes as All Dark Matter

TL;DR

The paper addresses whether primordial black holes can constitute all dark matter in light of new microlensing and related constraints. It advances a double-inflation mechanism that produces a sharply peaked small-scale power spectrum, and develops an extended-mass-function framework to apply constraints to a continuous PBH spectrum. The key finding is that all-DM PBHs remain viable only near $M_* \approx 10^{20}$ \mathrm{g}$ with $\sigma \lesssim 0.1$, supported by a concrete parameter set yielding $\Omega_{PBH,tot} = \Omega_c$. This work links inflationary dynamics to dark matter, offering testable predictions (e.g., second-order gravitational waves) and highlighting how future observations could confirm or exclude this scenario.

Abstract

Following a new microlensing constraint on primordial black holes (PBHs) with $\sim10^{20}$--$10^{28}\,\mathrm{g}$~[1], we revisit the idea of PBH as all Dark Matter (DM). We have shown that the updated observational constraints suggest the viable mass function for PBHs as all DM to have a peak at $\simeq 10^{20}\,\mathrm{g}$ with a small width $σ\lesssim 0.1$, by imposing observational constraints on an extended mass function in a proper way. We have also provided an inflation model that successfully generates PBHs as all DM fulfilling this requirement.

Figures (3)

• Figure 1: Black thick line: $\Omega_\text{PBH} (M)$ for parameters given in Eq. \ref{['eq:prms']} is shown. We require the total abundance be equal to the observed DM density, $\Omega_\text{PBH,tot} = \Omega_c$. The solid lines with shades represent relevant observational constraints on the current PBH mass spectrum [class (a)]: extra-galactic gamma-ray (EG$\gamma$) Carr:2009jm, femtolensing (Femto) Barnacka:2012bm, existence of white dwarfs in our local galaxy (WD) Graham:2015apa, Subaru HSC microlensing (HSC) takada, Kepler milli/microlensing (Kepler) Griest:2013esa, EROS/MACHO microlensing (EROS/MACHO) Tisserand:2006zx, dynamical heating of ultra-faint dwarf galaxies (UFD) Brandt:2016aco, and X-ray/radio constraints Gaggero:2016dpq. The solid line without shade illustrates the observational constraints on the past PBH mass spectrum [class (b)]: accretion constraints by CMB Ali-Haimoud:2016mbvBlum:2016cjsHorowitz:2016lib. Here we do not show the pulsar timing array constraints Arzoumanian:2015lizLentati:2015qwpShannon:2015ect on gravitational waves via second order effects Saito:2008jcSaito:2009jtBugaev:2009zhBugaev:2010bb because they are indirect and depend on the concrete shape of the scalar power spectrum. Nevertheless, it is noticeable that their constraints are so strong that PBHs with $M \sim 0.75 \gamma M_\odot$--$75 \gamma M_\odot$ are excluded (See for instance Fig. 1 in Inomata:2016rbd), if they are generated via superhorizon fluctuations. See Inomata:2016rbdNakama:2016gzwOrlofsky:2016vbd for details. The conservative bound of the new HSC microlensing constraint is shown by the thick blue line with the deep shade, and the dotted one utilizes an extrapolation from the HST PHAT star catalogs in the disk region takada.
• Figure 2: Constraints on parameters $(M_\ast, \sigma, f_\text{PBH})$ of the extended mass function given in Eq. \ref{['eq:extended']}. Here we have adopted all the constraints shown in Fig. \ref{['fig:pbh']}. The region consistent with the full DM, $f_{\text{PBH}} = 1$, is inside the dashed line near $M_\ast \simeq 10^{20}$ g with $\sigma \lesssim 1$.
• Figure 3: Constraints on parameters of the extended mass function given in Eq. \ref{['eq:extended']} with $M_\ast \simeq 10^{20}$ g and $f_\text{PBH} = 1$. Orange dotted region is excluded by WD Graham:2015apa. Blue dotted region is excluded by HSC takada.