Nucleation of thick topological defects during inflation

Spherical domain-wall bubbles, circular loops of string, and monopole-antimonopole pairs can spontaneously nucleate in de Sitter space. Here we develop the formalism for finding the relevant instantons and obtain numerical solutions for the case of domain walls. We find that the instanton solutions exist only when the domain wall thickness δ is sufficiently small compared to the de Sitter horizon H-1. For our simple model, the maximum thickness is δmax=H-1/ √2 . The same phenomenon occurs for strings and monopoles. The regime where δ∼δmax is studied analytically and the value of δmax is calculated for all three types of defects