Discretisation parameter and operator ordering in loop quantum cosmology
  with the cosmological constant
  In loop quantum cosmology, the Hamiltonian reduces to a finite difference
operator. We study the initial singularity and the large volume limit against
the ambiguities in the discretisation and the operator ordering within a
homogeneous, isotropic and spatially flat model with the cosmological constant.
We find that the absence of the singularity strongly depends on the choice of
the operator ordering and the requirement for the absence singles out a very
small class of orderings. Moreover we find a general ordering rule required for
the absence of the singularity. We also find that the large volume limit
naturally recovers a smooth wave function in the discretisation where each step
corresponds to a fixed volume increment but not in the one where each step
corresponds to a fixed area increment. If loop quantum cosmology is to be a
phenomenological realisation of full loop quantum gravity, these results are
important to fix the theoretical ambiguities.
