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Onset of synchronization in coupled Mixmaster oscillators.

Spiros Cotsakis1,2

  • 1Institute of Gravitation and Cosmology, RUDN University, ul. Miklukho-Maklaya 6, Moscow 117198, Russia.

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|March 14, 2022
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Summary

Spatial points undergoing chaotic Mixmaster oscillations synchronize when coupled above a threshold. This early-time synchronization leads to simpler, unified states as the universe approaches the singularity.

Keywords:
generic singularityinhomogeneous Mixmaster evolutionsynchronization

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Area of Science:

  • Cosmology
  • Dynamical Systems
  • Astrophysics

Background:

  • The universe's approach to the initial singularity involves complex dynamics.
  • Mixmaster oscillations describe chaotic behavior in certain cosmological models.
  • Understanding synchronization in inhomogeneous spacetime is crucial for early-universe physics.

Purpose of the Study:

  • To investigate asymptotic synchronization of coupled spatial points in chaotic Mixmaster dynamics.
  • To determine the conditions and mechanisms for synchronization in inhomogeneous spacetime.
  • To explore the implications of synchronization for the universe's evolution towards the singularity.

Main Methods:

  • Analysis of coupled chaotic Mixmaster oscillations.
  • Identification of a synchronization threshold for spatial points.
  • Development of a Lyapunov function to quantify synchronization speed.
  • Derivation of a proof for mean-field interaction and spontaneous synchronization.

Main Results:

  • Synchronization occurs for coupled Mixmaster spatial points above a critical coupling value.
  • Synchronization synchronizes exponentially fast in the past direction.
  • A mean-field interaction mechanism drives spontaneous synchronization between spatial points.
  • Synchronization leads to a resetting effect, making distinct BKL maps converge.

Conclusions:

  • The universe tends towards simpler, synchronized states as it approaches the initial singularity.
  • Early-time inhomogeneous synchronization plays a significant role in the universe's organization.
  • These findings offer insights into the behavior of matter and spacetime near the Big Bang.