The loop quantum dynamics of Kantowski-Sachs and Bianchi-III LRS spacetimes with cosmological constant is studied in the effective spacetime description. We show that classical singularity is avoided, and replaced by bounces of the triads. Unlike the singularity resolution in other loop quantum spacetimes, evolution results in a spacetime which retains quantum curvature after the bounce on one side of the temporal evolution. In the asymptotic limit, a spacetime which is a direct product of two constant curvature spaces emerges. Interestingly, despite high curvature, the effective spacetime metric is a solution of Einstein field's equations albeit with a different stress energy tensor. For the Kantowski-Sachs case, the resulting spacetime is a 'charged' Nariai spacetime, and for the Bianchi-III LRS spacetime, one obtains anti-Bertotti-Robinson spacetime with an emergent cosmological constant. The emergent 'charge' and cosmological constant are purely quantum geometric in origin.
Publication Source (Journal or Book title)
14th Marcel Grossman Meeting On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories, Proceedings
Dadhich, N., Joe, A., & Singh, P. (2018). Emergence of product of constant curvature spaces in loop quantum cosmology. 14th Marcel Grossman Meeting On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories, Proceedings, 4048-4053. https://doi.org/10.1142/9789813226609_0540