It is well known that the spontaneous breaking of discrete symmetries may lead to conflict with big-bang cosmology. This is due to formation of domain walls which give unacceptable contribution to the energy density of the universe. On the other hand it is expected that gravity breaks global symmetries explicitly. In this work we propose that this could provide a natural solution to the domain-wall problem.

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In this paper, starting from a system of noninteracting spins in a plane and introducing an appropriate density function for spins, we arrive at a metric independent continuum chiral model. The Lagrangian of this model is a variant of the CP 1 Chern-Simons term and is characterized by an interesting variety of gauge and symmetry groups and topological features. Certain significant aspects of this model or variants thereof are also shared by the mean field approach to the anyon gas, the CP 1 model with the Chern-Simons term and the RVB description of the strongly coupled Hubbard model. The class of models studied here may therefore be useful in the investigation of the latter systems.

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