  We propose a method to extract predictions from quantum cosmology for
inflation that can be confronted with observations. Employing the tunneling
boundary condition in quantum geometrodynamics, we derive a probability
distribution for the inflaton field. A sharp peak in this distribution can be
interpreted as setting the initial conditions for the subsequent phase of
inflation. In this way, the peak sets the energy scale at which the
inflationary phase has started. This energy scale must be consistent with the
energy scale found from the inflationary potential and with the scale found
from a potential observation of primordial gravitational waves. Demanding a
consistent history of the universe from its quantum origin to its present
state, which includes decoherence, we derive a condition that allows one to
constrain the parameter space of the underlying model of inflation. We
demonstrate our method by applying it to two models: Higgs inflation and
natural inflation.
