Comparison of Loop quantum cosmology and Wheeler-DeWitt quantum cosmology.

Quantum geometrodynamics and loop quantum gravity are two canonical approaches to quantum gravity. Their corresponding cosmological theories, Wheeler-DeWitt quantum cosmology and loop quantum cosmology, give different results for the same cosmological model. We use a flat isotropic homogeneous universe coupled to a massless scalar field and calculate in both theories the quantized Hamiltonian constraint, the wave packets, the Hubble parameter, and the volume expectation value. We see that both, the Hubble parameter, and the volume expectation values, show different behaviour in LQC and WDW theory. We also look at the criticism about certain assumptions in LQC and comment on the singularity avoidance claims in LQC. To understand the criticism well, we calculate the quantum fluctuations of the volume operator.