Klein Bottle Cosmology

TL;DR

This paper investigates a higher-dimensional universe with Klein Bottle topology, revealing symmetry breaking, fermion condensates, and potential implications for matter-antimatter asymmetry in cosmology.

Contribution

It introduces a novel cosmological model with Klein Bottle topology that explicitly breaks key symmetries and explores its effects on fermion condensates and CP violation.

Findings

Klein Bottle topology breaks translational and CP symmetries.

Fermion condensate wall is localized in the Klein Bottle.

Potential mechanism for matter-antimatter asymmetry.

Abstract

We explore a higher-dimensional universe that is a product of Minkowski space and the non-orientable 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.