Domain Wall Formation In The Post-Inflationary Universe

Abstract

We consider the evolution of the probability distribution $\text{pp}(\chi ,\text{chib},\text{t})$, 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, $\text{pp}$ 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.

Comments: 12pages