Non-singular AdS-dS transitions in a landscape scenario
  Understanding transitions between different vacua of a multiverse allowing
eternal inflation is an open problem whose resolution is important to gain
insights on the global structure of the spacetime as well as the problem of
measure. In the classical theory, transitions from the anti-deSitter to
deSitter vacua are forbidden due to the big crunch singularity. In this
article, we consider toy landscape potentials: a double well and a triple well
potential allowing anti-deSitter and de-Sitter vacua, in the effective dynamics
of loop quantum cosmology for the $k=-1$ FRW model. We show that due to the
non-perturbative quantum gravity effects as understood in loop quantum
cosmology, non-singular anti-deSitter to de-Sitter transitions are possible. In
the future evolution, an anti-deSitter bubble universe does not encounter a big
crunch singularity but undergoes a big bounce occurring at a scale determined
by the underlying quantum geometry. These non-singular transitions provide a
mechanism through which a probe or a `watcher', used to define a local measure,
can safely evolve through the bounce and geodesics can be smoothly extended
from anti-deSitter to de-Sitter vacua.
