Jul 5 – 10, 2021
Europe/Rome timezone

Asymptotic synchronization of Mixmaster spatial points

Jul 5, 2021, 4:30 PM
Invited talk in the parallel session Topological methods, global existence problems, and spacetime singularities Topological Methods, Global Existence Problems, and Spacetime Singularities


Spiros Cotsakis (Univ. Aegean, Greece; IGC, RUDN Univ., Moscow, Russia)


We consider the problem of asymptotic synchronization of different spatial points coupled to each other in inhomogeneous spacetime and undergoing chaotic Mixmaster oscillations towards the singularity. We demonstrate that for couplings larger than some threshold value, two Mixmaster spatial points $A,B$, with $A$ in the past of $B$, synchronize and thereby proceed in perfect unison towards the initial singularity. We further show that there is a Lyapunov function for the synchronization dynamics that makes different spatial points able to synchronize exponentially fast in the past direction. We provide an elementary proof of how an arbitrary spatial point responds to the mean field created by the oscillators, leading to their direct interaction through spontaneous synchronization. These results ascribe a clear physical meaning of early-time synchronization, the two BKL maps corresponding to two distinct oscillating spatial points converge to each other and become indistinguishable at the end of synchronization, and suggest that the universe organizes itself gradually through simpler, synchronized, states as it approaches the initial singularity. A discussion of further implications of early-time inhomogeneous Mixmaster synchronization for the horizon problem and the behavior of entropy is also provided.

Primary author

Spiros Cotsakis (Univ. Aegean, Greece; IGC, RUDN Univ., Moscow, Russia)

Presentation materials