  The quantum description of time evolution in non-linear gravitational systems
such as cosmological space-times is not well understood. We show, in the
simplified setting of mini-superspace, that time evolution of this system can
be obtained using a gauge fixed path integral, as long as one does not
integrate over proper time. Using this gauge fixed action we can construct a
Hamiltonian in the coherent - or classical - state basis. We show that by
construction the coherent states satisfy the classical dynamical equations of
General Relativity. They do not satisfy the Hamiltonian constraint. A
consequence of this is that the Wheeler-DeWitt equation should not be satisfied
in quantum gravity. Classical states have a natural non-trivial time evolution
since they are not eigenstates of the Hamiltonian. A general feature of the
unconstrained quantum theory of gravity is the prediction of a pressureless
dark matter component of either sign energy density in the classical universe
which may lead to novel phenomenology.
