Anisotropic models in loop quantum cosmology with the Gambini-Benítez-Pullin polymerization

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-Benítez-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.