Symmetry of the physical space and quantum cosmological description for non-minimally coupled scalar field cosmology

Noether symmetry analysis as well as symmetries of the physical space has been investigated for non-minimally coupled scalar field cosmology in the background of flat Friedmann–Lemaître–Robertson–Walker (FLRW) space–time. The Noether symmetry analysis not only identifies the symmetry vector but also the conserved charge associated with this symmetry. Canonical quantization scheme (for quantum cosmology) has been used to formulate the Wheeler-DeWitt equation and solutions are obtained using separable form of the wave function. Finally, quantum Bohmian trajectories has been formulated using causal interpretation and their classical limits has been examined.