Non-metric Quantum Cosmology
  Scalar-tensor theory has arbitrary functions of the scalar field in front of the geometric and scalar terms in the Lagrangain. The extent to which these arbitrary functions appear in the Wheeler-deWitt wavefunction of mini-super Robertson-Walker spacetimes is discussed. The function of the scalar field in front of the Einstein-Hilbert action allows a current to be constructed which suggests transfer from matter to geometry of aspects of the wavefunction. 
Mark D. Roberts
gr-qc