Primordial Black Hole Formation in Dust-Radiation Bouncing Cosmologies

TL;DR

This paper develops a framework to study primordial black hole formation in dust-radiation bouncing cosmologies, finding that PBH production is highly suppressed due to the small curvature perturbations and collapse conditions.

Contribution

It introduces a unified semi-analytical approach to evaluate PBH formation in dust-radiation bouncing models, accounting for two-fluid collapse dynamics and threshold criteria.

Findings

Critical curvature threshold is nearly mass-independent and extremely small.

Curvature power spectrum amplitude is too small for significant PBH formation.

Radiation pressure and two-fluid collapse conditions suppress PBH production.

Abstract

Primordial black holes (PBHs) provide a unique probe of the early Universe and may have an enhanced abundance in bouncing cosmologies, where a long contracting phase can amplify perturbations. We develop a unified framework to study PBH formation in dust-radiation bouncing cosmologies, focusing on the classical contracting phase so that the results are insensitive to bounce details. We compute the curvature power spectrum for an extremely small dust equation of state using a stable semi-analytical (adiabatic) method, derive the Jeans length of the two-fluid system using dynamical-system analysis and the WKB approximation, and extend the three-zone model from the single- to the two-fluid case to model local collapse. We implement two collapse criteria to obtain the curvature perturbation threshold for PBH formation and estimate PBH mass fractions for benchmark masses spanning low-mass ($10^{-17} M_{\odot}$) to supermassive ($10^{13} M_{\odot}$) scales. The critical curvature threshold is extremely small and nearly mass-independent over a broad range $(\zeta_c \sim 10^{-21}$ for $10^{-14}$ to $10^{13} M_{\odot})$, with deviations only near dust-radiation equality. Nevertheless, the square root of the curvature power spectrum at the relevant formation times is many orders of magnitude smaller, yielding vanishingly small PBH mass fractions across the benchmark masses. Compared with the pure-dust case, radiation pressure and the two-fluid collapse conditions significantly suppress PBH production, implying that substantial PBH formation in dust-radiation bouncing cosmologies would require additional mechanisms to amplify curvature perturbations.