Quantum cosmology in coupled Brans–Dicke gravity: A Noether symmetry analysis

This work deals with a multi-field cosmological model in a spatially flat FLRW spacetime geometry. The usual Brans–Dicke (BD) field and another scalar field are minimally coupled to gravity while they interact with each other through the Kinetic terms. The main aim of this work is to examine whether the model is compatible with cosmic observations. So cosmological solutions are obtained using symmetry analysis only. By imposing Noether Symmetry to the Lagrangian of the system, the potential of the scalar field as well as the coupling function had been determined. The classical solutions are determined after simplifying the Lagrangian using cyclic variables. Finally, Wheeler–DeWitt (WD) equation in quantum cosmology has been formulated and conserved momenta corresponding to Noether symmetry will show the periodic part of the wave function and it helps to have the complete integral for the wave function.