We compare the path integral for transition functions in unimodular gravity
    and in general relativity. In unimodular gravity the cosmological constant is a
    property of states that are specified at the boundaries whereas in general
    relativity the cosmological constant is a parameter of the action. Unimodular
    gravity with a nondynamical background spacetime volume element has a time
    variable that is canonically conjugate to the cosmological constant. Wave
    functions depend on time and satisfy a Schr\”odinger equation. On the contrary,
    in the covariant version of unimodular gravity with a 3-form gauge field,
    proposed by Henneaux and Teitelboim, wave functions are time independent and
    satisfy a Wheeler-DeWitt equation, as in general relativity. The 3-form gauge
    field integrated over spacelike hypersurfaces becomes a “cosmic time” only in
    the semiclassical approximation. In unimodular gravity the smallness of the
    observed cosmological constant has to be explained as a property of the initial

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