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Real scalar field kink(-antikink)s and their perturbation spectra in a closed universe

In this paper we demonstrate that solitons of a simple real scalar field model that are {\it static and linearly stable} do exist when considered in a (3+1)-dimensional, spatially compact space-time background, the static Einstein universe, which is a good approximation to the observed universe for sufficiently small time intervals. We study the properties of these solutions for a $Φ^4$-potential and demonstrate that next to the fundamental solutions, excited configurations exist. We also investigate general perturbations about the solitons, determine their eigenfrequency spectra and compare them with those of the perturbations about the vacua of the model. We find that the degeneracy with respect to the multipoles of the perturbation, which is present for the vacua, does no longer exist in the presence of the soliton. Moreover, specific perturbations correspond to zero modes of the system. Our results have applications in condensed matter physics as well as computations of quantum effects (e.g. the Casimir energy) in spatially compact space-times in the presence of soliton-like objects.