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. Analysing the time evolution of planar domain walls and of global monopoles, we find that the defects undergo inflationary expansion if $η\stackrel{>}{\sim}0.33m_{Pl}$, where $η$ is the vacuum expectation value of the Higgs field and $m_{Pl}$ 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.