Revisiting Unimodular Quantum Cosmology

Quantization of unimodular gravity in minisuperspace leads to a time evolution of states generated by the Hamiltonian, as in usual quantum mechanics. We revisit the analysis made by Unruh, extending it to phantom scalar fields. It is argued that only in this case a nontrivial evolution for the scalar field can be obtained. The behavior of the scale factor presents a bounce followed by de Sitter expansion, reproducing the quantum cosmological scenario in General Relativity when the source is given by a cosmological term described by the Schutz variable. The analysis is extended to the Brans–Dicke scalar-tensor theory.