Chaos of Yang-Mills Field in Class A Bianchi Spacetimes
arXiv:gr-qc/0412060 · doi:10.1103/PhysRevD.71.064007
Abstract
Studying Yang-Mills field and gravitational field in class A Bianchi spacetimes, we find that chaotic behavior appears in the late phase (the asymptotic future). In this phase, the Yang-Mills field behaves as that in Minkowski spacetime, in which we can understand it by a potential picture, except for the types VIII and IX. At the same time, in the initial phase (near the initial singularity), we numerically find that the behavior seems to approach the Kasner solution. However, we show that the Kasner circle is unstable and the Kasner solution is not an attractor. From an analysis of stability and numerical simulation, we find a Mixmaster-like behavior in Bianchi I spacetime. Although this result may provide a counterexample to the BKL (Belinskii, Khalatnikov and Lifshitz) conjecture, we show that the BKL conjecture is still valid in Bianchi IX spacetime. We also analyze a multiplicative effect of two types of chaos, that is, chaos with the Yang-Mills field and that in vacuum Bianchi IX spacetime. Two types of chaos seem to coexist in the initial phase. However, the effect due to the Yang-Mills field is much smaller than that of the curvature term.
15 pages, 8 figures
References in corpus (9)
- The mixmaster universe is chaotic
- The mixmaster universe: A chaotic Farey tale
- Chaotic Friedmann-Robertson-Walker Cosmology
- Relativistic chaos is coordinate invariant
- Mixmaster chaos
- Chaos in the Einstein-Yang-Mills Equations
- How to determine approximate Mixmaster parameters from numerical evolution of Einstein's equations
- FRW cosmologies between chaos and integrability
- Axially Symmetric Bianchi I Yang-Mills Cosmology as a Dynamical System
Cited by in corpus (12)
- Cosmology with inhomogeneous magnetic fields
- Classical and Quantum Features of the Mixmaster Singularity
- Anisotropic Inflation with Non-Abelian Gauge Kinetic Function
- Cosmologies in Horndeski's second-order vector-tensor theory
- Inflationary Dynamics with a Non-Abelian Gauge Field
- Non-chaotic dynamics in general-relativistic and scalar-tensor cosmology
- Revised research about chaotic dynamics in Manko et al. spacetime
- Cosmological Co-evolution of Yang-Mills Fields and Perfect Fluids
- Chaos-order transition in Bianchi I non-Abelian Born-Infeld cosmology
- Phantom cosmology as a scattering process
- Global dynamics of Yang-Mills field and perfect-fluid Robertson-Walker cosmologies
- Non-Abelian condensates as alternative for dark energy