On the Weyl Curvature Hypothesis

TL;DR

This paper explores the Weyl curvature hypothesis in cosmology, demonstrating that a broad class of singularities, including generalized models beyond standard isotropic ones, satisfy Penrose's conjecture about low entropy at the Big Bang.

Contribution

It extends Einstein's equations to include a class of singularities and shows that these satisfy the Weyl curvature hypothesis in generalized cosmological models.

Findings

The extended Einstein's equations remain valid at important singularities.

Generalized cosmological models' Big-Bang singularities satisfy the Weyl curvature hypothesis.

The approach encompasses models beyond standard isotropic and homogeneous universes.

Abstract

The Weyl curvature hypothesis of Penrose attempts to explain the high homogeneity and isotropy, and the very low entropy of the early universe, by conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity. In previous papers it has been proposed an equivalent form of Einstein's equation, which extends it and remains valid at an important class of singularities (including in particular the Schwarzschild, FLRW, and isotropic singularities). Here it is shown that if the Big-Bang singularity is from this class, it also satisfies the Weyl curvature hypothesis. As an application, we study a very general example of cosmological models, which generalizes the FLRW model by dropping the isotropy and homogeneity constraints. This model also generalizes isotropic singularities, and a class of singularities occurring in Bianchi cosmologies. We show that the Big-Bang singularity of this model is of the type under consideration, and satisfies therefore the Weyl curvature hypothesis.