The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Roger Penrose in an article in 1979[1] in an attempt to provide explanations for two of the most fundamental issues in physics.
Penrose suggests that the resolution of both of these problems is rooted in a concept of the entropy content of gravitational fields.
Penrose associates the initial low entropy content of the universe or the past hypothesis with the effective vanishing of the Weyl curvature tensor of the cosmological gravitational field near the Big Bang.
Mathematical treatments of Penrose's ideas on the Weyl curvature hypothesis have been given in the context of isotropic initial cosmological singularities e.g. in the articles.
[2][3][4][5] Penrose views the Weyl curvature hypothesis as a physically more credible alternative to cosmic inflation (a hypothetical phase of accelerated expansion in the early life of the universe) in order to account for the presently observed almost spatial homogeneity and isotropy of our universe.