Nucleation rates for tunneling processes in Minkowski and de Sitter space are investigated, taking into account one loop prefactors. In particular, we con- sider the creation of membranes by an antisymmetric tensor field, analogous to Schwinger pair production. This can be viewed as a model for the decay of false (or true) vacuum at zero temperature, in the thin wall limit. Also considered is the spontaneous nucleation of strings, domain walls and monopoles during inflation. The instantons for these processes are spherical world-sheets or world-lines embedded in flat or de Sitter backgrounds. We find the contribution of such instantons to the semiclassical partition function, including one loop corrections due to small fluctuations around the spherical worldsheet. We sug- gest a prescription for obtaining the distribution of objects nucleated during inflation. This can be seen as an extension of the usual formula, valid in flat space, according to which the nucleation rate is twice the imaginary part of the free energy. In addition, we use the method of Bogolubov transformations to compute the rate of pair production by an electric field in 1+1 dimensional de Sitter space, and compare the results to those obtained using the instanton me- thod. Both results agree where they are expected to, not only in the exponen- tial dependence but also in the prefactor, confirming the validity of instanton techniques in de Sitter space. Throughout the paper, both the gravitational field and the antisymmetric tensor field are assumed external.

57 pages, TUTP-10-93