Klein Bottle Cosmology

Abstract

We explore a higher-dimensional universe that is a product of Minkowski space and the nonorientable Klein bottle. The topology explicitly breaks important symmetries, such as translational invariance and (5+1)-dimensional CP invariance. Somewhat surprisingly, the (3+1)-dimensional cp of the Minkowski space can also be broken by the Klein bottle, both explicitly and in the presence of a brane. The topology enforces a background of fermion correlations that amounts to a condensate wall localized in the Klein bottle. The wall acts as an order parameter for the broken symmetries. If a brane passes through the wall, brane fermions that couple to the condensate are produced as quantified by the Bogoliubov coefficients for a time-dependent mass. The scenario meets the conditions, including cp violation, to potentially generate the matter-antimatter asymmetry of the universe.