No cosmological domain wall problem for weakly coupled fields

After inflation occurs, a weakly coupled scalar field will in general not be in thermal equilibrium but have a distribution of values deter-mined by the inflationary Hubble parameter. If such a field subsequently undergoes discrete symmetry breaking, then the different degenerate vacua may not be equally populated so the domain walls which form will be biased and the wall network will subsequently collapse. Thus the cosmological domain wall problem may be solved for sufficiently weakly coupled fields in a post inflationary universe. We quantify the criteria for determining whether this does happen, using a Higgs-like potential, with a spontaneously broken Z(2) symmetry.