On Cosmological Isotropy, Quantum Cosmology and the Weyl Curvature Hypothesis

TL;DR

This paper explores how signature change and Weyl curvature hypotheses relate to the universe's isotropy, flatness, and initial inflation, proposing that certain conditions lead to homogeneous, isotropic cosmologies like de Sitter space.

Contribution

It links signature change models with Weyl curvature hypotheses, showing how they imply isotropy, inflation, and specific cosmological solutions such as the Vilenkin tunnelling universe.

Findings

Signature change models imply initial inflation and isotropy.

Adding electric Weyl curvature restricts solutions to homogeneous, isotropic universes.

In the cosmological-constant case, the solution is the de Sitter universe.

Abstract

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.