Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe
arXiv:2105.00647 · doi:10.1103/PhysRevD.104.024006
Abstract
The Belinski-Khalatnikov-Lifshitz (BKL) conjecture predicts a chaotic alternation of Kasner epochs in the evolution of generic classical spacetimes towards a spacelike singularity. As a first step towards understanding the full quantum BKL scenario, we analyze a vacuum Bianchi II model with local rotational symmetry, which presents just one Kasner transition. During the Kasner epochs, the quantum state is coherent and it is thus characterized by constant values of the different quantum fluctuations, correlations and higher-order moments. By computing the constants of motion of the system we provide, for any peaked semiclassical state, the explicit analytical transition rules that relate the parametrization of the asymptotic coherent state before and after the transition. In particular, we obtain the modification of the transition rules for the classical variables due to quantum back-reaction effects. This analysis is performed by considering a high-order truncation in moments (the full computations are performed up to fifth-order, which corresponds to neglecting terms of an order ), providing a solid estimate about the quantum modifications to the classical model. Finally, in order to understand the dynamics of the state during the transition, we perform some numerical simulations for an initial Gaussian state, that show that the initial and final equilibrium values of the quantum variables are connected by strong and rapid oscillations.
Version accepted in PRD. Minor typos corrected
References in corpus (13)
- A covariant approach for perturbations of rotationally symmetric spacetimes
- The Bianchi IX model in Loop Quantum Cosmology
- A Hamiltonian Formulation of the BKL Conjecture
- Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
- Statistical moments for classical and quantum dynamics: formalism and generalized uncertainty relations
- A new proof of the Bianchi type IX attractor theorem
- Classical and quantum behavior of the harmonic and the quartic oscillators
- New class of LRS spacetimes with simultaneous rotation and spatial twist
- Fluctuation energies in quantum cosmology
- Rotating and twisting locally rotationally symmetric spacetimes: a general solution
- Rotating and twisting locally rotationally symmetric imperfect fluids
- Quantum theory of the Bianchi II model
- Classical versus quantum evolution for a universe with a positive cosmological constant