Isotropic singularities and the Penrose-Weyl tensor hypothesis

According to Penrose's Weyl tensor hypothesis (1979), an appropriate boundary condition to impose at any initial singularity is that the Weyl tensor should vanish there. Cosmological models that admit isotropic singularities provide a mathematical framework for studying this hypothesis. Tod (1957) has conjectured that, within the isotropic singularity framework, the only models that satisfy the Penrose boundary condition are the exact FRW models. The author discusses the relationship of this conjecture to an earlier one of Goode and Wainwright (1985), and reduces the proof of Tod's conjecture to establishing uniqueness of solution to an appropriate initial value problem.