Toward fixing a framework for conformal cyclic cosmology

TL;DR

This paper critically compares various proposed methods for selecting the conformal factor in conformal cyclic cosmology, aiming to resolve inconsistencies and introduce a new class of solutions aligned with Penrose's assumptions.

Contribution

It systematically analyzes existing models for the conformal factor in CCC, rules out some proposals, corrects previous calculations, and introduces a new solution class consistent with Penrose's framework.

Findings

Certain proposed conformal factors are incompatible with Penrose's assumptions.

Corrections to Newman’s calculations resolve previous inconsistencies.

A new class of solutions satisfying Penrose's conditions is proposed.

Abstract

Conformal Cyclic Cosmology (CCC) is a cyclic model of the universe put forward by Sir Roger Penrose. 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, Tod and Nurowski, 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.