A description of classical and quantum cosmology for a single scalar field torsion gravity

In the background of homogeneous and isotropic flat FLRW space-time, both classical and quantum cosmology has been studied for teleparallel dark energy (DE) model. Using Noether symmetry analysis, not only the symmetry vector but also the coupling function in the Lagrangian and the potential of the scalar field has been determined. Also symmetry analysis identifies a cyclic variable in the Lagrangian along the symmetry vector and as a result the Lagrangian simplifies to a great extend so that classical solution is obtained. Subsequently, in quantum cosmology Wheeler-DeWitt(WD) equation has been constructed and the quantum version of the conserved momenta corresponding to Noether symmetry identifies the periodic part of the wave function of the universe and as a result the Wheeler-DeWitt equation becomes solvable. Finally, quantum description shows finite non-zero probability at the classical big-bang singularity.
Comment: 16 Pages, 4 figures