Bianchi I model in terms of nonstandard loop quantum cosmology: Classical dynamics

TL;DR

This paper analyzes the classical dynamics of the Bianchi I universe within a nonstandard loop quantum cosmology framework, showing how holonomy modifications can remove singularities but introducing a free parameter.

Contribution

It provides a classical analysis of Bianchi I in loop quantum cosmology, deriving observables and demonstrating singularity removal through holonomy modifications.

Findings

Holonomy modifications remove classical singularities.

The model introduces a free parameter not fixed by the theory.

Classical observables are constructed from elementary variables.

Abstract

The cosmological singularities of the Bianchi I universe are analyzed in the setting of loop geometry underlying the loop quantum cosmology. We solve the Hamiltonian constraint of the theory and find the Lie algebra of elementary observables. Physical compound observables are defined in terms of elementary ones. Modification of classical theory by holonomy around a loop removes the singularities. However, our model has a free parameter that cannot be determined within our method. Testing the model by the data of observational cosmology may be possible after quantization of our modified classical theory.