Separate Universes Do Not Constrain Primordial Black Hole Formation

Understand

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.