Cosmological discrete self-similarity in primordial black hole formation

TL;DR

This paper shows that discrete self-similarity, previously observed in flat spacetime collapse, also appears in primordial black hole formation in an expanding universe, affecting mass scaling and gravitational wave predictions.

Contribution

It demonstrates the survival of discrete self-similarity in cosmological PBH formation through relativistic simulations, revealing detailed oscillation structures in mass scaling.

Findings

Log-periodic oscillations in PBH mass scaling relation.

Differences in oscillation structure compared to flat spacetime case.

Critical exponents and DSS periods are consistent across initial data types.

Abstract

We demonstrate that discrete self-similarity (DSS), originally discovered in the collapse of a massless scalar field in an asymptotically flat system, survives in primordial black hole (PBH) formation within an expanding cosmological background. Using fully relativistic numerical simulations of massless scalar-field collapse in an Friedmann-Lema\^{i}tre-Robertson-Walker universe, we resolve the critical regime down to $|p-p_c|\sim 10^{-8}$, where $p$ and $p_c$ respectively are a parameter of the family of initial data and its threshold value, and find clear log-periodic oscillations in the PBH mass scaling relation. The detailed structure of these oscillations differs from that previously reported in the asymptotically flat case, exhibiting a more pronounced asymmetry between peaks and troughs. Analyzing two distinct families of initial data (Gaussian and piecewise rational curvature profiles), we find critical exponents and DSS periods that differ slightly but are broadly consistent within uncertainties. The presence of DSS implies characteristic log-periodic modulations in the PBH mass spectrum, with potential consequences for PBH abundances and the spectrum of induced gravitational waves.