On cosmological isotropy, quantum cosmology and the Weyl curvature hypothesis

The increasing entropy, large-scale isotropy and approximate flatness of the universe are considered in the context of signature change, which is a classical model of quantum tunnelling in quantum cosmology. The signature change hypothesis implies an initial inflationary epoch, the magnetic half of the Weyl curvature hypothesis, and a close analogue of the conformal singularity hypothesis. Adding the electric half of the Weyl curvature hypothesis yields, for a perfect fluid, only homogeneous isotropic cosmologies. In the cosmological-constant case, the unique solution is the Vilenkin tunnelling solution, which gives a de Sitter cosmology.