Thick Domain Wall Universes

We investigate the spacetime of a thick gravitating domain wall for a general potential V (Φ). Using general analytical arguments we show that all nontrivial solutions fall into two categories: those interpretable as an isolated domain wall with a cosmological event horizon, and those which are pure false vacuum de Sitter solutions. Although this latter solution is always unstable to the field rolling coherently to its true vacuum, we show that there is an additional instability to wall formation if the scalar field does not couple too strongly to gravity. Using the λΦ4 and sine-Gordon models as illustrative examples, we investigate the phase space of the gravitating domain wall in detail numerically, following the solutions from weak to strong gravity. We find excellent agreement with the analytic work. Then, we analyse the domain wall in the presence of a cosmological constant (of either sign) finding again the two kinds of solutions. Finally we show that as a consequence of this phase transition, the false vacuum solution cannot be perturbed in a way that would allow us to interpret it as the inflating core of a topological defect. PACS numbers: 04.80.-b, 11.27.+d, 98.80.Cq DTP/99/5 gr-qc/9902081 Typeset using REVTEX E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected] 1