- Letter
- Access by Xinjiang University
Cosmological discrete self-similarity in primordial black hole formation
Phys. Rev. D 114, L041307 – Published 28 August, 2026
DOI: https://doi.org/10.1103/58r5-8zng
Abstract
We demonstrate that discrete self-similarity (DSS), originally discovered in the asymptotically flat collapse of a massless scalar field, survives in primordial black hole (PBH) formation within an expanding cosmological background. Using fully relativistic simulations of massless scalar-field collapse in a Friedmann-Lemaître-Robertson-Walker universe, we resolve the near-critical regime and find clear log-periodic oscillations in the PBH mass-scaling relation. This result provides a proof of principle that PBHs may retain information about the critical behavior in their formation realized in the early Universe: PBH formation in scalar-field kination exhibits DSS, while radiation-fluid collapse is characterized by continuous self-similarity. The resulting mass scaling imprints characteristic log-periodic modulations in an illustrative PBH mass spectrum, which may survive when PBH formation is dominated by a sufficiently narrow range of scales, with possible consequences for PBH phenomenology. Our results show that PBHs may encode not only the amplitude of primordial perturbations, but also the nature of the matter sector and the dynamical state of the Universe at horizon reentry.
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