Conformal scalar fields, isotropic singularities and conformal cyclic cosmologies

Abstract

We analyse spacetimes with a conformal scalar field source, a cosmological constant and a quartic self-interaction term for the scalar field. We also consider additional matter contents in the form of Maxwell and Yang-Mills fields or radiation fluids. Existence theorems for weakly asymptotically flat spacetimes are given. We give a generalisation of Bekenstein's result [Ann. Phys. 82, 535 (1974)] and use it to derive existence theorems for spacetimes that contain an isotropic singularity. The results are combined to suggest a mathematical setup for Penrose's CCC scenario using a conformal scalar field cosmology.

18 pages, 2 figures

References in corpus (2)

• A Fundamental Solution to the CCC equation
• Astrophysical black holes may radiate, but they do not evaporate

Cited by in corpus (1)

• Conformal Methods in General Relativity with application to Conformal Cyclic Cosmology: A minicourse given at the IXth IMLG Warsaw 2018