Semiclassical study of the Mixmaster model: the quantum Kasner map
arXiv:2207.00566 · doi:10.1103/PhysRevD.106.064051
Abstract
According to the Belinski-Khalatnikov-Lifshitz conjecture, close to a spacelike singularity different spatial points decouple, and the dynamics can be described in terms of the Mixmaster (vacuum Bianchi IX) model. In order to understand the role played by quantum-gravity effects in this context, in the present work we consider the semiclassical behavior of this model. Classically, this system undergoes a series of transitions between Kasner epochs, which are described by a specific transition law. This law is derived based on the conservation of certain physical quantities and the rotational symmetry of the system. In a quantum scenario, however, fluctuations and higher-order moments modify these quantities, and consequently also the transition rule. In particular, we perform a canonical quantization of the model and then analytically obtain the modifications of this transition law for semiclassical states peaked around classical trajectories. The transition rules for the quantum moments are also obtained, and a number of interesting properties are derived concerning the coupling between the different degrees of freedom. More importantly, we show that, due to the presence of quantum-gravity effects and contrary to the classical model, there appear certain finite ranges of the Kasner parameters for which the system will not undergo further transitions and will follow a Kasner regime until the singularity. Even if a more detailed analysis is still needed, this feature points toward a possible resolution of the classical chaotic behavior of the model. Finally, a numerical integration of the equations of motion is also performed in order to verify the obtained analytical results.
arXiv comment32 pages. Minor changes, version accepted for publication
References in corpus (35)
- Effective Equations of Motion for Quantum Systems
- Loop quantum cosmology of Bianchi type IX models
- Numerical Approaches to Spacetime Singularities
- The Bianchi IX attractor
- The mixmaster universe: A chaotic Farey tale
- Loop quantum cosmology of Bianchi type II models
- Numerical simulations of generic singuarities
- The Bianchi IX model in Loop Quantum Cosmology
- High-order quantum back-reaction and quantum cosmology with a positive cosmological constant
- A Hamiltonian Formulation of the BKL Conjecture
- Spike Oscillations
- Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
- Effective potentials from semiclassical truncations
- Statistical moments for classical and quantum dynamics: formalism and generalized uncertainty relations
- Singularity avoidance in a quantum model of the Mixmaster universe
- Smooth Quantum Dynamics of Mixmaster Universe
- Inhomogeneous Quantum Mixmaster: from Classical toward Quantum Mechanics
- Effective Dynamics in Bianchi Type II Loop Quantum Cosmology
- A new proof of the Bianchi type IX attractor theorem
- Classical and quantum behavior of the harmonic and the quartic oscillators
- Minisuperspace models as infrared contributions
- Quantum Belinski-Khalatnikov-Lifshitz scenario
- Polymer representation of the Bianchi IX Cosmology in the Misner variables
- On the dynamics of the general Bianchi IX spacetime near the singularity
- Canonical description of cosmological backreaction
- Spectral properties of the quantum Mixmaster universe
- A quantum gravity extension to the Mixmaster dynamics
- Fluctuation energies in quantum cosmology
- Do spikes persist in a quantum treatment of spacetime singularities?
- Mixmaster Revisited: Wormhole Solutions to the Bianchi IX Wheeler-DeWitt Equation using the Euclidean-Signature Semi-Classical Method
- Quantum Geometrodynamics of the Bianchi IX cosmological model
- Minisuperspace models of discrete systems
- Quantum theory of the Bianchi II model
- Classical versus quantum evolution for a universe with a positive cosmological constant
- Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe