Abstract
Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive black holes. The mechanism of black hole formation described in this paper is very generic and has important implications for the global structure of the universe. Baby universes inside super-critical black holes inflate eternally and nucleate bubbles of all vacua allowed by the underlying particle physics. The resulting multiverse has a very non-trivial spacetime structure, with a multitude of eternally inflating regions connected by wormholes. If a black hole population with the predicted mass spectrum is discovered, it could be regarded as evidence for inflation and for the existence of a multiverse.
Highlights
Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe
We studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally
We have explored the cosmological consequences of a population of spherical domain walls and vacuum bubbles which may have nucleated during the last N ∼ 60 e-foldings of inflation
Summary
We describe the gravitational collapse of bubbles after inflation, when they are embedded in the matter distribution of a FRW universe. Three different time scales will be relevant for the dynamics. Where ρm is the matter density, the scale associated with the vacuum energy inside the bubble, tb ≡ Hb−1 = (3/8πGρb)1/2,. The acceleration time-scale due to the repulsive gravitational field of the domain wall tσ ≡ Hσ−1 = (2πGσ)−1. The relation (2.4) guarantees that the repulsive gravitational force due to the vacuum energy and wall tension are subdominant effects at the end of inflation, and can only become important much later. The dynamics of spherically symmetric vacuum bubbles has been studied in the thin wall limit by Berezin, Kuzmin and Tkachev [8].4. Ρi is the vacuum energy outside the bubble, R is the radius of the bubble wall, and R ≡ dR/dτ , where τ is the proper time on the bubble wall worldsheet, at fixed angular position. Eq (2.5) can be interpreted as an energy conservation equation.
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