Toward fixing a framework for conformal cyclic cosmology

Abstract

Conformal Cyclic Cosmology (CCC) is a cyclic model of the universe put forward by Sir Roger Penrose (Cycles of Time: An Extraordinary New View of the Universe, Random House, Manhattan, 2010). A conformal invariance assumption in the neighbourhood of the crossover region between cycles (which Penrose calls aeons) allows successive space-times to be related by a conformal rescaling. A major open problem is how to choose the conformal factor in a unique way, and is a fundamental hurdle to further study. Proposals have been put forward by Newman (Gen Relativ Gravit 46(5):1–13, 2014), Tod (Gen Relativ Gravit 47(3):1–13, 2015) and Nurowski (Class Quantum Gravity 38(14):145004, 2021), but they disagree in one way or another with Penrose’s original assumptions as well as each other. In this paper we compare these different models in detail and rule out certain choices for the conformal factor that have been put forward by Penrose. We extend the results of Newman and fix inconsistencies that arose in his calculations. A new class of solutions are put forward which agree with Penrose’s assumptions exactly so long as a certain additional relation is satisfied.