Nucleation of thick topological defects during inflation

Abstract

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 $\ensuremath{\delta}$ is sufficiently small compared to the de Sitter horizon ${H}^{\ensuremath{-}1}$. For our simple model, the maximum thickness is ${\ensuremath{\delta}}_{max}=\frac{{H}^{\ensuremath{-}1}}{\sqrt{2}}$. The same phenomenon occurs for strings and monopoles. The regime where $\ensuremath{\delta}\ensuremath{\approx}{\ensuremath{\delta}}_{max}$ is studied analytically and the value of ${\ensuremath{\delta}}_{max}$ is calculated for all three types of defects.