  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 and isotropic
cosmologies. In the cosmological-constant case, the unique solution is the
Vilenkin tunnelling solution, which gives a de Sitter cosmology.
