Primordial black holes: constraints, potential evidence and prospects

TL;DR

Primordial black holes (PBHs) are explored as dark matter candidates, GW sources, and SMBH progenitors, with emphasis on how extended mass functions and formation mechanisms shape their observational signatures. The paper develops a comprehensive framework linking PBH formation to mass functions, evaporation history, and multi-messenger constraints from evaporation, lensing, dynamics, accretion, and gravitational waves, including scalar-induced GWs and PBH-binary mergers. It highlights potential evidence hints across several channels and projects the near-future reach of LVK, PTAs, LISA, ET, AEDGE, and X-ray missions to probe asteroid- to solar-mass PBHs, as well as the viability of extended mass-function constraints. Publicly available digitized constraint tables for extended mass functions are provided, enabling precise evaluation of PBH scenarios against current data. The work underscores that PBHs remain testable across a broad mass range, with gravitational-wave observations and SIGWs offering particularly promising avenues for discovery or exclusion in the coming decade.

Abstract

Primordial black holes (PBHs) may have formed in the early Universe and may account for all or part of the dark matter. In this review, we summarize the current observational constraints on PBHs across the full mass range, highlight potential evidence for their existence, and outline the prospects for future searches, particularly with gravitational-wave observatories. We also discuss different PBH formation scenarios, identify the corresponding mass functions, and present the observational constraints in each case.

Figures (9)

• Figure 1: Left panel: Broad mass functions obtained from critical collapse, including the effect of the QCD phase transition. The solid line is given by the ansatz in Eq. \ref{['Eq:QCD']}, while the dashed line is computed assuming a broad power spectrum as in Eq. \ref{['eq:Broad']}. Right panel: Narrow mass functions obtained from critical collapse with the QCD phase transition included (bright lines) and omitted (faded lines). The solid lines are given by Eq. \ref{['Eq:QCD']} while dashed lines are numerically computed assuming a log-normal power spectrum with width $\Delta=0.3$ centered at $k_* = 6\cdot10^{6}$ Mpc$^{-1}$ (blue) and $k_* = 2 \times 10^{6}$ Mpc$^{-1}$ (red). In both panels, the mass functions are normalized by $\int {\rm d} \ln M_{\rm PBH} \, \psi(M_{\rm PBH}) = 1$.
• Figure 2: Left panel: Broad (solid) and narrow (dashed) mass functions resulting respectively from a broad power spectrum (with $k_{\rm min}=10^{6}$${\rm Mpc}^{-1}$ and $k_{\rm max} =10^{14.5}$${\rm Mpc}^{-1}$) and a log-normal power spectrum (with $\Delta=0.5$ and $k_{\rm *}=6 \times 10^{12}$${\rm Mpc}^{-1}$) with different realisations of the NG in the curvaton model, i.e. different $r_{\rm dec}$ (see Ref. Ferrante:2023bgz for more details of the model). The amplitude of the power spectrum has been re-scaled for each $r_{\rm dec}$ such that PBHs comprise the totality of DM. Right panel: Height of the peak at the QCD scale for different $r_{\rm dec}$. We choose the benchmark points $k_{{ \rm min}}=10^{6}$${\rm Mpc}^{-1}$ (red) and $k_{{ \rm min}}=10^{5}$${\rm Mpc}^{-1}$ (blue) respectively. The plot shows a decreasing trend of $\psi_{\rm Solar}\equiv \psi(1M_{\odot})$ when $r_{\rm dec}$ increases, resulting from the effect of NG reducing the abundance of high masses. The dashed lines represent the height of the peak at the QCD scale, computed by taking into account only non-linearities. The mass functions are normalized in order to get the main peak at $m\simeq 5\times 10^{-14}M_{\odot}$. In both panels, the mass functions are normalized by $\int {\rm d} \ln M_{\rm PBH} \, \psi(M_{\rm PBH}) = 1$.
• Figure 3: Left panel: Amplitudes for a broken power-law curvature spectrum (Eq. \ref{['eq:BPLPS']}) required to have $f_{\rm PBH}=1$ for the curvaton model (red solid line) and the USR-like model (blue solid line), using the full NG relation, while the dashed line shows the results using the quadratic approximation. We assume $\alpha=4$, $\beta=3$, $\gamma=1$, $k_*=10^7$ Mpc$^{-1}$ and $\delta_{\rm th}=0.55$.
• Figure 4: Compilation of constraints for monochromatic PBH mass functions (bold) and some relevant potential evidence (dashed) (SNE Smirnov:2022zip, OGLE Niikura:2019kqi, LVK Andres-Carcasona:2024wqk). Only the dominant constraint in each mass range is labelled. The vertical dashed line on the left indicates the PBH mass that would complete its evaporation today, while the vertical dashed line on the right corresponds to the horizon mass at the time of CMB formation.
• Figure 5: The solid curves show the constraints for critical-collapse mass functions \ref{['eq:psicc0']} (upper left), log-normal mass function \ref{['eq:psiln']} with $\sigma=1$ (upper rigtht), and truncated power-law mass function $\psi \propto M_{\rm PBH}^\alpha$ with $\alpha = -1$ (lower left) and $\alpha = 1$ (lower right). The dashed curves show the constraints for monochromatic mass functions.