From Cosmic Bounces to Primordial Black Holes: The Role of Primordial Magnetic Fields

Abstract: We investigate primordial black hole (PBH) formation from primordial magnetic fields generated during a non-singular ekpyrotic bounce. A time-dependent coupling between the electromagnetic field and a scalar background breaks conformal invariance and amplifies gauge field fluctuations during contraction, generating magnetic fields whose anisotropic stress dominates during radiation domination. By retaining finite-wavenumber cutoffs, we compute the ultraviolet-dominated curvature spectrum, evaluate density-perturbation variance, and determine PBH abundances using both monochromatic and critical-collapse prescriptions. For benchmark parameters, the critical collapse mass spectrum peaks at $M\simeq 2.0\times10<sup>{-3}M_\odot$ , with a total PBH dark matter fraction of $f_{PBH}\approx 10<sup>{-5}$, forming a subdominant subsolar PBH population. Enforcing the cosmological overclosure bound ($f_{\mathrm{PBH}} \le 1$) constrains the primary background parameters, namely the end-of-contraction Hubble scale ($$H_{\mathrm{end}} \le 1.6 \times 10<sup>3~\mathrm{GeV}$$) and the contraction exponent ($q \le 0.247$), establishing a physical boundary consistent with the electromagnetic backreaction limit. Shifting to asteroid-mass PBHs or a larger dark matter fraction requires modifying the ultraviolet cutoff and contraction duration. This analysis highlights the essential role of finite-wavenumber cutoffs and assumed-collapse prescriptions in linking bounce magnetogenesis to the predicted PBH abundance.