Dynamics of topological defects and inflation

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 η≳0.33m_p1, where η is the vacuum expectation value of the Higgs field and m_p1 is the Planck mass. This result confirms the estimates by Vilenkin and Linde. The critical value of η is independent of the coupling constant λ 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 η 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.