[Paper Review] Primordial Black Holes

Albert Escrivà, Florian Kühnel+1 more|arXiv (Cornell University)|Nov 10, 2022

Cosmology and Gravitation Theories28 citations

TL;DR

This review discusses how primordial black holes form in the early universe, their role as dark matter candidates, and their gravitational-wave and other observational signatures, focusing on formation thresholds and related physics.

ABSTRACT

Aspects of primordial black holes, i.e. black holes formed in the early Universe, are reviewed. Special emphasis is put on their formation, their role as dark matter candidates and their manifold signatures, particularly through gravitational waves.

Motivation & Objective

• Motivate PBHs as natural dark matter candidates and probes of early-universe physics.
• Explain the formation mechanism from inflationary perturbations and the collapse dynamics.
• Define and analyze the collapse threshold and its dependence on perturbation profiles and equation of state.
• Outline observable signatures and constraints across gravitational waves, lensing, and astrophysical data.

Proposed method

• Use the Misner–Sharp formalism to model spherically symmetric collapse of cosmological perturbations.
• Define the compaction function and identify the PBH formation threshold δc from its peak (δm = C(rm)).
• Apply gradient-expansion techniques to relate superhorizon curvature perturbations to hydrodynamic quantities.
• Examine dependence of δc on curvature-profile shape (K(r) or ζ(˜r)) and on the equation of state w.
• Discuss analytical threshold estimates and numerical schemes for threshold estimation and PBH abundance.
• Link curvature perturbations to inflationary power spectra and discuss inflationary scenarios that produce PBHs.

Experimental results

Research questions

• RQ1 How does the PBH formation threshold δc depend on the curvature-profile shape and the equation of state?
• RQ2 What is the relation between curvature perturbations during inflation and the resulting PBH mass function?
• RQ3 How do type-I and type-II fluctuations differ in their PBH formation and what are their observational implications?
• RQ4 What are the main observational signatures and constraints on PBHs across gravitational waves, lensing, and cosmology?

Key findings

• The PBH formation threshold δc depends on the curvature-profile shape parameter q and the equation of state w, with sharper profiles (higher q) yielding larger δc while softer profiles yield smaller δc.
• Threshold values are robust across different profiles with the same q to within a few percent, showing a strong profile-geometry dependence.
• Type-I fluctuations dominate PBH formation, while Type-II fluctuations, though possible at high amplitudes, are typically less relevant for abundance.
• Apparent-horizon formation marks the onset of PBH growth, with initial PBH mass determined at horizon-entry and subsequent accretion influencing final mass.
• Analytical estimates of δc can match numerical results in certain regimes, with nontrivial dependence on w and profile choice, necessitating numerical methods in other regimes.
• PBHs naturally connect to inflationary physics, allowing PBH observations to probe early-Universe dynamics and phase transitions.