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 determined 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.