A conjecture about the general cosmological solution of Einstein's equations

Abstract

We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We conjecture that, on approach to a singularity, the interaction of spacetime Mixmaster oscillations in different regions of an inhomogeneous universe can produce a synchronisation of these oscillations through a coupling to their mean field in the way first demonstrated by the Kuramoto coupled oscillator model.

arXiv comment7 pages, no figures, added analysis

References in corpus (9)

• The Bianchi IX attractor
• The past attractor in inhomogeneous cosmology
• Curvature blow up in Bianchi VIII and IX vacuum spacetimes
• The Kuramoto Model with Time-Varying Parameters
• Kuramoto dynamics in Hamiltonian systems
• Spike Oscillations
• On the initial value problem for second order scalar fluctuations in Einstein static
• Mathematical General Relativity
• Perturbations and Linearization Stability of Closed Friedmann Universes

Cited by in corpus (6)

• Generalization of the Gauss Map: A jump into chaos with universal features
• A Scenario for a Singularity-free Generic Cosmological Solution
• Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework
• Multifractality in the general cosmological solution of Einstein's equations
• Structural stability and general relativity
• Onset of synchronization in coupled Mixmaster oscillators