Penrose's Weyl curvature hypothesis and conformally-cyclic cosmology

I discuss two ideas of Roger Penrose and the relation between them: his Weyl curvature hypothesis from thirty years ago and his recent idea for a conformally-cyclic universe, that is a cosmological model with positive cosmological constant in which the conformal metric is cyclic – it can be continued through the future null infinity of one aeon to the big bang of the following aeon.

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