  The existence of a quantum bounce in isotropic spacetimes is a key result in
loop quantum cosmology (LQC), which has been demonstrated to arise in all the
models studied so far. In most of the models, the bounce has been studied using
numerical simulations involving states which are sharply peaked and which
bounce at volumes much larger than the Planck volume. An important issue is to
confirm the existence of the bounce for states which have a wide spread, or
which bounce closer to the Planck volume. Numerical simulations with such
states demand large computational domains, making them very expensive and
practically infeasible with the techniques which have been implemented so far.
To overcome these difficulties, we present an efficient hybrid numerical scheme
using the property that at the small spacetime curvature, the quantum
Hamiltonian constraint in LQC, which is a difference equation with uniform
discretization in volume, can be approximated by a Wheeler-DeWitt differential
equation. By carefully choosing a hybrid spatial grid allowing the use of
partial differential equations at large volumes, and with a simple change of
geometrical coordinate, we obtain a surprising reduction in the computational
cost. This scheme enables us to explore regimes which were so far unachievable
for the isotropic model in LQC. Our approach also promises to significantly
reduce the computational cost for numerical simulations in anisotropic LQC
using high performance computing.
