Spherical domain wall collapse in a dust universe

To clarify the observational consequences of bubble nucleations in an inflationary era, we analyze the dynamics of a spherical domain wall in an expanding universe. We consider a spherical shell of the domain wall with tension collapsing in a spherically symmetric dust universe, which is initially separated into the open Friedmann-Lemaître-Robertson-Walker universe inside the shell and the Einstein-de Sitter universe outside. The domain wall shell collapses due to the tension, and sweeps the dust fluid out. The universe after the collapse becomes inhomogeneous and is described by the Lemaître-Tolman-Bondi model. We construct solutions describing this inhomogeneous universe by solving dynamical equations obtained from Israel's junction conditions applied to this system. We find that a black hole forms after the domain wall collapse for any initial condition, and that the black hole mass at the moment of its formation is universally given by , where is the Hubble parameter at the time when the shell radius becomes equal to the Hubble radius. We also find that the dust fluid is distributed as near the central region after the collapse, where R is the area radius. These features would provide observable signatures of a spherical domain wall generated in the early universe.