[gpsx]

Gravity is similar to an electric field here. A wave function for a field consists of an amplitude for each field configuration, where a “field configuration” refers to a value for the electric field for each point in space. In GR each field configuration would correspond to a space time geometry for the universe. We have quantized excitations as distinct “valid” solutions to the wave function, which we call a particle, though it is nothing like an electron. The notion of space time geometry holds throughout. (Edit: in practice, people never calculate wave functions for fields like electric fields. That would be too hard. Different methods are used in calculations. Second edit: the wave function wouldn’t be composed of complete space-time configurations, histories of the universe, but time slices from it, like space geometries. Maybe this can be expanded in responses/comments.)