NUCLEATION RATES IN FLAT AND CURVED SPACE

Nucleation rates for tunneling processes in Minkowski and de Sitter sp ace are investigated, taking into account one loop prefactors. In part icular, we consider the creation of membranes by an antisymmetric tens or field, analogous to Schwinger pair production.. This can be viewed as a model for the decay of a false (or true) vacuum at zero temperatu re in the thin wall limit. Also considered is the spontaneous nucleati on of strings, domain walls, and monopoles during inflation. The insta ntons for these processes are spherical world sheets or world lines em bedded in flat or de Sitter backgrounds. We find the contribution of s uch instantons to the semiclassical partition function, including the one loop corrections due to small fluctuations around the spherical wo rld sheet. We suggest a prescription for obtaining, from the partition function, the distribution of objects nucleated during inflation. Thi s can be seen as an extension of the usual formula, valid in flat spac e, according to which the nucleation rate is twice the imaginary part of the free energy. For the case of pair production, the results repro duce those that can be obtained using second quantization methods, con firming the validity of instanton techniques in de Sitter space. Throu ghout the paper, both the gravitational field and the antisymmetric te nsor field are assumed external.