Dynamics of false vacuum bubbles: beyond the thin shell approximation

We numerically study the dynamics of false vacuum bubbles which are inside an almost flat background; we assumed spherical symmetry and the size of the bubble is smaller than the size of the background horizon. According to the thin shell approximation and the null energy condition, if the bubble is outside of a Schwarzschild blackhole, unless we assume Farhi-Guth-Guven tunneling, expanding and inflating solutions are impossible. In this paper, we extend our method to beyond the thin shell approximation: we include the dynamics of fields and assume that the transition layer between a true vacuum and a false vacuum has non-zero thickness. If a shell has sufficiently low energy, as expected from the thin shell approximation, it collapses (Type 1). However, if the shell has sufficiently large energy, it tends to expand. Here, via the field dynamics, field values of inside of the shell slowly roll down to the true vacuum and hence the shell does not inflate (Type 2). If we add sufficient exotic matters to regularize the curvature near the shell, inflation may be possible without assuming Farhi-Guth-Guven tunneling. In this case, a worm hole is dynamically generated around the shell (Type 3). By tuning our simulation parameters, we could find transitions between Type 1 and Type 2, as well as between Type 2 and Type 3. Between Type 2 and Type 3, we could find another class of solutions (Type 4). Finally, we discuss the generation of a bubble universe and the violation of unitarity. We conclude that the existence of a certain combination of exotic matter fields violates unitarity.