Dynamics of Topological Defects and Inflation

TL;DR

This paper investigates the conditions under which topological defects like domain walls and monopoles undergo inflation, confirming that a critical Higgs field value triggers inflation regardless of initial defect size or coupling constants.

Contribution

It provides a detailed analysis of defect dynamics, confirming the critical Higgs vacuum expectation value for inflation and exploring gauge field effects on monopole spacetime.

Findings

Defects inflate if η ≳ 0.33 m_Pl, independent of coupling or initial size.

Gauge monopoles have attractive spacetime, unlike global monopoles.

Inflation onset is unaffected by defect initial size if η exceeds critical value.

Abstract

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 $\eta\stackrel{>}{\sim}0.33m_{Pl}$, where $\eta$ 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 $\eta$ is independent of the coupling constant $\lambda$ 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 $\eta$ 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.