  For many years, the most active area of quantum cosmology has been the issue
of choosing boundary conditions for the wave function of a universe. Recently,
loop quantum cosmology, which is obtained from loop quantum gravity, has shed
new light on this question. In this case, boundary conditions are not chosen by
hand with some particular physical intuition in mind, but they are part of the
dynamical law. It is then natural to ask if there are any relations between
these boundary conditions and the ones provided before. After discussing the
technical foundation of loop quantum cosmology which leads to crucial
differences to the Wheeler-DeWitt quantization, we compare the dynamical
initial conditions of loop quantum cosmology with the tunneling and the
no-boundary proposal and explain why they are closer to the no-boundary
condition. We end with a discussion of recent developments and several open
problems of loop quantum cosmology.
