Domain walls in a FRW universe.

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 {ital H}{equivalent_to}{ital H}/{ital m}{ge}1/2, where {ital H} is the Hubble parameter and {ital m} is the scalar mass. In the general FRW case we develop a systematic perturbative expansion in {ital 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 {ital negative} at the core of the defect for some values of the nonminimal 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 Minkowskimore » spacetime.« less