Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology

TL;DR

This paper develops effective dynamics in Bianchi I loop quantum cosmology, showing multiple big bounces and revealing scaling symmetries that connect quantum geometry with temporal evolution.

Contribution

It introduces two improved strategies for implementing LQC corrections in Bianchi I models and analyzes their implications for big bounces and scaling symmetries.

Findings

Big bounces occur up to three times in each spatial direction.

Two different schemes show distinct sensitivities to boundary conditions.

Scaling symmetries suggest a link between quantum geometry and time.

Abstract

The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to three times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.