Domain Walls in a FRW Universe

Abstract

We solve the equations of motion for a scalar field with domain wall boundary conditions in a Friedmann-Robertson-Walker (FRW) spacetime. We find (in agreement with Basu and Vilenkin) that no domain wall solutions exist in de Sitter spacetime for h = H/m >= 1/2, where H is the Hubble parameter and m is the scalar mass. In the general FRW case we develop a systematic perturbative expansion in h to arrive at an approximate solution to the field equations. We calculate the energy momentum tensor of the domain wall configuration, and show that the energy density can become negative at the core of the defect for some values of the non-minimal coupling parameter xi. We develop a translationally invariant theory for fluctuations of the wall, obtain the effective Lagrangian for these fluctuations, and quantize them using the Bunch-Davies vacuum in the de Sitter case. Unlike previous analyses, we find that the fluctuations act as zero-mass (as opposed to tachyonic) modes. This allows us to calculate the distortion and the normal-normal correlators for the surface. The normal-normal correlator decreases logarithmically with the distance between points for large times and distances, indicating that the interface becomes rougher than in Minkowski spacetime.