  Topological defects can be formed during inflation by phase transitions as
well as by quantum nucleation. We study the effect of the expansion of the
Universe on the internal structure of the defects. We look for stationary
solutions to the field equations, i.e. solutions that depend only on the proper
distance from the defect core. In the case of very thin defects, whose core
dimensions are much smaller than the de Sitter horizon, we find that the
solutions are well approximated by the flat space solutions. However, as the
flat space thickness parameter $\delta_0$ increases we notice a deviation from
this, an effect that becomes dramatic as $\delta_0$ approaches $(H)^{-1}/{\sqrt
2}$. Beyond this critical value we find no stationary solutions to the field
equations. We conclude that only defects that have flat space thicknesses less
than the critical value survive, while thicker defects are smeared out by the
expansion.
