Effective LQC model for k=+1 isotropic cosmologies from spatial discretisations

TL;DR

This paper develops an effective Loop Quantum Cosmology model for closed (k=+1) isotropic universes, showing that quantum gravity effects resolve singularities and cause only minor deviations from classical recollapse.

Contribution

It introduces a full Thiemann regularisation for the scalar constraint in k=+1 LQC, providing an effective model that captures quantum effects on closed cosmologies.

Findings

Singularities are resolved in the effective model.

Classical recollapse persists with minor quantum corrections.

The model accurately reflects qualitative quantum gravity effects.

Abstract

The closed, spatially isotropic FLRW universe (k=+1) is endowed with modifications due to a discrete underlying space-structure. Motivated from Loop Quantum Gravity techniques, a full Thiemann regularisation is performed. The impact of these modifications of the single-graph-sector appearing in the scalar constraint are interpreted as physical quantum gravity effects. We investigate the form of the modified scalar constraint and its analytical approximations for k=+1 spacetimes and assume this effective constraint as the generator of dynamics on the reduced isotropic phase space. It transpires that the system still features a classical recollapse with only marginal discreteness corrections. Moreover, the initial and final singularities are resolved and we present an effective model mirroring the qualitative features of system.