Separate Universes Do Not Constrain Primordial Black Hole Formation

TL;DR

This paper challenges previous constraints on primordial black hole formation, showing that the maximum fluctuation size is a geometric effect rather than a physical limit, and explores the dynamics beyond this maximum.

Contribution

It demonstrates that the maximum fluctuation size is a geometric artifact, not a physical constraint, and analyzes the evolution of larger initial curvature fluctuations in black hole formation.

Findings

The maximum fluctuation size arises from slicing geometry, not physical limits.

A volume fluctuation variable diverges for separate universes on superhorizon scales.

The dynamics of larger initial fluctuations differ from smaller ones, as shown in spacetime diagrams.

Abstract

Carr and Hawking showed that the proper size of a spherical overdense region surrounded by a flat FRW universe cannot be arbitrarily large as otherwise the region would close up on itself and become a separate universe. From this result they derived a condition connecting size and density of the overdense region ensuring that it is part of our universe. Carr used this condition to obtain an upper bound for the density fluctuation amplitude with the property that for smaller amplitudes the formation of a primordial black hole is possible, while larger ones indicate a separate universe. In contrast, we find that the appearance of a maximum is not a consequence of avoiding separate universes but arises naturally from the geometry of the chosen slicing. Using instead of density a volume fluctuation variable reveals that a fluctuation is a separate universe iff this variable diverges on superhorizon scales. Hence Carr's and Hawking's condition does not pose a physical constraint on density fluctuations. The dynamics of primordial black hole formation with an initial curvature fluctuation amplitude larger than the one corresponding to the maximum density fluctuation amplitude was previously not considered in detail and so we compare it to the well-known case where the amplitude is smaller by presenting embedding and conformal diagrams of both types in dust spacetimes.