On the Weyl Curvature Hypothesis
  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.
