Nucleation of vacuum phase transitions by topological defects

The Euclidean action is calculated in the thin-wall approximation for a first-order vacuum phase transition in which the bubble appears symmetrically around either a global monopole or a gauge cosmic string. The bubble is assumed to be much larger than the core size of the monopole or string. In both cases the value of the Euclidean action is shown to be reduced below the O(4) symmetric action value, indicating that the topological defects act as effective nucleation sites for vacuum decay. Over the last two decades, vacuum phase transitions have evolved from being an oddity in electroweak theory to being an expected part of the early universe, likely responsible for inflation, and possibly the source of exotic topological structures such as domain wall, strings, and monopoles. In addition, there is also the disquieting possibility that we live in a metastable false vacuum state today, the decay of which would be the ultimate natural catastrophe. The Euclidean action approach to calculating vacuum decay rates was first developed in the thin-wall approximation by Coleman [1]. While subsequent investigation has shown that the thin-wall approximation is only truly valid for a very small set of potentials [2], it is always valid in the ultimate limit wherein the true and false vacuum states are nearly degenerate in energy. There are two ways in which this near degeneracy may be achieved in the real universe. First, as the universe expands and cools, every potential will pass through a state of degeneracy, due to the thermal terms in the potential; for a broad variety of potentials, the phase transition from false to true vacuum will take place while the potential is nearly degenerate. In this case, the thin-wall approximation may still be sufficiently valid to yield an adequate approximation to the true Euclidean action. Secondly, if the false and true vacuum are truly nearly degenerate at zero temperature (which results in an extremely long decay time for the false vacuum–conceivably even as long as 10 years) then the thin-wall approximation is obviously valid. In this letter the Euclidean action for a thin-wall bubble nucleating symmetrically around a global monopole or a gauge cosmic string is calculated. The spacetime metric is taken to be that appropriate for the exterior region of a global monopole or gauge string and is fixed. The gravitational effects of the vacuum energy density are ignored; they will not substantially influence the value of the action unless the symmetry breaking scale is comparable to the Planck energy [3]. The energy scale of the vacuum phase transition is assumed to be substantially lower than that which is responsible for the topological defect; this assures that the core region of the monopole or string is only a negligible fraction of the nucleating bubble’s interior volume. The symmetry breaking which created the global monopole or cosmic string is assumed to be independent of the phase transition under consideration; Preskill and Vilenkin have considered the opposite case in which the vacuum phase transition affects the symmetry groups whose quotient defines the topological defects [4]. The presence of the global monopole or gauge cosmic string