  Despite the ultraviolet problems with canonical quantum gravity, as an
effective field theory its infrared phenomena should enjoy fully quantum
mechanical unitary time evolution. Currently this is not possible, the
impediment being what is known as the problem of time. Here, we provide a
solution by promoting the cosmological constant $\Lambda$ to a Lagrange
multiplier constraining the metric volume element to be manifestly a total
derivative. Because $\Lambda$ appears linearly in the Hamiltonian constraint,
it unitarily generates time evolution, yielding a functional Schroedinger
equation for gravity. Two pleasant side effects of this construction are that
vacuum energy is dissociated from the cosmological constant problem, much like
in unimodular gravity, and the natural foliation provided by the time variable
defines a sensible solution to the measure problem of eternal inflation.
