Through the big bang: Continuing Einstein's equations beyond a cosmological singularity

Tim A. Koslowski (Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Cd. Universitaria, Ciudad de México, D.F., 04510, Mexico) ; Flavio Mercati (Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada; Dipartimento di Fisica, UniversitÃ di Roma âLa Sapienzaâ, P.le A. Moro 2, Roma, 00185, Italy) ; David Sloan (Beecroft Institute of Particle Astrophysics and Cosmology, Department of Physics, University of Oxford, Denys Wilkinson Building, 1 Keble Road, Oxford, OX1 3RH, UK)

All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics – it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

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Published on:
03 February 2018
Publisher:
Elsevier
Published in:
Physics Letters B (2018)

DOI:
https://doi.org/10.1016/j.physletb.2018.01.055