Anisotropic models in LQC with GBP polymerisation

TL;DR

This paper explores anisotropic loop quantum cosmology models using Gambini-Benítez-Pullin polymerisation, analyzing their bounce behavior, curvature, and density properties, with implications for black hole interiors and cosmological evolution.

Contribution

It applies GBP polymerisation to anisotropic models, revealing how minimal area constraints influence bounce dynamics and singularity avoidance in different geometries.

Findings

Bounce occurs with positive density and negative pressures.

Oscillatory solutions with re-collapse in Kantowski-Sachs space.

Asymptotically flat space-times with bounce in Bianchi III.

Abstract

Polymer models are effective in describing quantum gravity effects around the initial singularity, leading to its replacement by bouncing surfaces on which the curvature and densities are finite. Their properties depend on the space-time symmetry and on the particular polymerisation scheme adopted. In this article we investigate anisotropic models under the Gambini-Ben\'itez-Pullin polymerisation, recently used to quantise spherically symmetric black-holes, whose interiors are isometric to Kantowski-Sachs (KS) space-times. Demanding that the minimum area defined by the bouncing surface matches the Loop Quantum Gravity area gap, we can find its radius alongside the curvature and effective density and pressures at the bounce. The density is always positive, while the pressures are negative enough to avoid the singularity. Due to the positive spatial curvature, the solution is oscillatory, reaching a maximum radius where a re-collapse occurs. Therefore, a positive cosmological constant is included in order to have an eternal expansion to a late de Sitter phase. We have also considered a Bianchi III metric, showing that the bounce is still present, but the space-time is asymptotically flat in this case, with no re-collapse. In this hyperbolic space, the minimal area constraint can also be imposed on compact $2$-surfaces. Nevertheless, in contrast to the KS case, it is enough for avoiding the singularity, independently of polymerisation procedures.