Physics
Scientific paper
Nov 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..44.3052s&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 44, Issue 10, 15 November 1991, pp.3052-3061
Physics
19
Particle-Theory And Field-Theory Models Of The Early Universe, Spontaneous Breaking Of Gauge Symmetries
Scientific paper
The self-gravity of quantum fields is often considered to be a negligible perturbation upon a background spacetime and not of much physical interest. Its importance is determined by the ratio of the mass of the field to the Planck mass, this ratio being very small for those fields that we are most familiar in dealing with. However, it is conceivable that either in the very early Universe or even today a false-vacuum decay could occur associated with a field of appreciable mass. The effect of self-gravity upon false-vacuum decay was initially studied within the ``thin-wall'' approximation by Coleman and De Luccia. Their analysis involved the approximate solution of the coupled Euclideanized field and Einstein equations with the assumption of O(4)-symmetric bubble nucleation. In this paper we consider the range of validity of the ``thin-wall'' approximation by comparing the Coleman-De Luccia results with exact numerical results for a quartic polynomial potential. We also extend the analysis into regimes for which the ``thin-wall'' approximation is inapplicable. In the case of an initially de Sitter space decaying into Minkowski space, we find a smooth transition between the Coleman-De Luccia mode of bubble formation and the Hawking-Moss transition, wherein the entire spacetime tunnels ``at once'' to the maximum of the potential. In the case of the decay of an initially Minkowski space to an anti-de Sitter space, we find that there is a ``forbidden region'' of vacuum potential parameters for which decay is not possible. At energies far below the Planck scale, the boundary of this region is accurately described by the thin-wall prediction obtained by Coleman and De Luccia. At energies near the Planck scale, however, the actual ``forbidden region'' is significantly smaller than predicted by the thin-wall approximation; thus, vacuum decays are possible which appear to be forbidden by thin-wall calculations. In all cases, the inclusion of gravitational effects tends to thicken the wall of the bubble.
Hiscock William A.
Samuel David A.
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