Spatially flat quantum cosmology

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Abstract
The authors investigate the quantum cosmology of spatially locally homogeneous cosmological models with flat compact spatial surfaces in three and four spacetime dimensions. In (2+1) dimensions the only possible spatial surfaces are the 2-torus and the Klein bottle, whereas in (3+1) dimensions there are ten possible spatial surfaces. The metric ansatz is kept in its most general form compatible with Hamiltonian mini-superspace dynamics. They find that the no-boundary proposal of Hartle and Hawking (1983) is applicable, at the semiclassical level, in both of the (2+1)-dimensional models but in only six of the (3+1)-dimensional models.

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