Can topological defects be formed during preheating ?

We study the dynamics of a scalar field \Phi with the potential g(|\Phi|^2-\eta^2)^2/2 (g=self-coupling constant, \eta=symmetry breaking scale) after inflation and make clear whether topological defects can ever be formed during preheating. In particular, we pay attention to GUT defects (\eta \sim 10^{15}GeV - 10^{17}GeV), and consider three types of fluctuations. The first one is produced due to parametric resonance, the second is due to the negative curvature of the potential, and the last is created during inflation. We search for the parameter region that nonthermal fluctuations of the scalar field produced through the parametric resonant decay of its homogeneous part do not lead to defect formation. We find that this region is rather wide, and the GUT defects are not produced after inflation. This fact shows that the positiveness of the effective mass square of the field and production of large fluctuations whose amplitude is as large as that of homogeneous mode are not enough conditions for full symmetry restoration.Comment: 10 pages, RevTex, 17 postscript figures included. The version to be published in Physical Review