Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe

TL;DR

This paper investigates quantum effects on the classical Kasner transition in a symmetric Bianchi II universe, deriving analytical transition rules and demonstrating quantum back-reaction impacts through high-order moment truncations and numerical simulations.

Contribution

It provides the first analytical quantum transition rules for a Bianchi II model with local rotational symmetry, including quantum back-reaction effects, advancing understanding of quantum cosmological singularity behavior.

Findings

Quantum back-reaction modifies classical transition rules.

Analytical transition rules derived for quantum states.

Numerical simulations show rapid oscillations during transitions.

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 $\hbar^3$), 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.