Dynamics of topological defects and inflation

Abstract

We study the dynamics of topological defects in the context of ``topological inflation'' proposed by Vilenkin and Linde independently. Analyzing the time evolution of planar domain walls and of global monopoles, we find that the defects undergo inflationary expansion if \ensuremath{\eta}\ensuremath{\gtrsim}0.33${\mathit{m}}_{\mathrm{Pl}}$, where \ensuremath{\eta} is the vacuum expectation value of the Higgs field and ${\mathit{m}}_{\mathrm{Pl}}$ is the Planck mass. This result confirms the estimates by Vilenkin and Linde. The critical value of \ensuremath{\eta} is independent of the coupling constant \ensuremath{\lambda} and the initial size of the defect. Even for defects with an initial size much greater than the horizon scale, inflation does not occur at all if \ensuremath{\eta} is smaller than the critical value. We also examine the effect of gauge fields for static monopole solutions and find that the spacetime with a gauge monopole has an attractive nature, contrary to the spacetime with a global monopole. It suggests that gauge fields affect the onset of inflation. \textcopyright{} 1996 The American Physical Society.