Emergence of product of constant curvature spaces in loop quantum
  cosmology
  The loop quantum dynamics of Kantowski-Sachs spacetime and the interior of
higher genus black hole spacetimes with a cosmological constant has some
peculiar features not shared by various other spacetimes in loop quantum
cosmology. As in the other cases, though the quantum geometric effects resolve
the physical singularity and result in a non-singular bounce, after the bounce
a spacetime with small spacetime curvature does not emerge in either the
subsequent backward or the forward evolution. Rather, in the asymptotic limit
the spacetime manifold is a product of two constant curvature spaces.
Interestingly, though the spacetime curvature of these asymptotic spacetimes is
very high, their effective metric is a solution to the Einstein's field
equations. Analysis of the components of the Ricci tensor shows that after the
singularity resolution, the Kantowski-Sachs spacetime leads to an effective
metric which can be interpreted as the `charged' Nariai, while the higher genus
black hole interior can similarly be interpreted as anti Bertotti-Robinson
spacetime with a cosmological constant. These spacetimes are `charged' in the
sense that the energy momentum tensor that satisfies the Einstein's field
equations is formally the same as the one for the uniform electromagnetic
field, albeit it has a purely quantum geometric origin. The asymptotic
spacetimes also have an emergent cosmological constant which is different in
magnitude, and sometimes even its sign, from the cosmological constant in the
Kantowski-Sachs and the interior of higher genus black hole metrics. With a
fine tuning of the latter cosmological constant, we show that `uncharged'
Nariai, and anti Bertotti-Robinson spacetimes with a vanishing emergent
cosmological constant can also be obtained.
