  An improved Hamiltonian constraint operator is introduced in loop quantum
cosmology. Quantum dynamics of the spatially flat, isotropic model with a
massless scalar field is then studied in detail using analytical and numerical
methods. The scalar field continues to serve as `emergent time', the big bang
is again replaced by a quantum bounce, and quantum evolution remains
deterministic across the deep Planck regime. However, while with the
Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce
can occur even at low matter densities, with the new Hamiltonian constraint it
occurs only at a Planck-scale density. Thus, the new quantum dynamics retains
the attractive features of current evolutions in loop quantum cosmology but, at
the same time, cures their main weakness.
