Domain Wall Formation In The Post-Inflationary Universe

We consider the evolution of the probability distribution $\pp (\chi ,\chib, \t)$, associated with an inhomogeneous light scalar field $\chi$ in the Robertson-Walker Universe, where the inhomogeneities are produced by quantum fluctuations during an earlier inflationary epoch. For a specific choice of scalar potential which occurs in models of so called late-time phase transitions in which domain walls are produced, $\pp$ is shown to evolve from a Gaussian to a non-Gaussian distribution. The structure of the latter justifies the recent use of 3-dimensional percolation theory to describe the initial distribution of domain walls in these models.