  In this thesis, we try to resolve the alleged problem of non-unitarity for
various anisotropic cosmological models. Using Wheeler-DeWitt formulation, we
quantized the anisotropic models with variable spatial curvature, namely
Bianchi II and Bianchi VI. We showed that Hamiltonian of respective models
admits self-adjoint extension, thus unitary evolution. We further extended the
unitary evolution for higher dimensional anisotropic cosmological models. We
also showed that unitarity of the model preserves the Noether symmetry but
loses the scale invariance. In later part of this thesis, we showed the
equivalence of Jordan and Einstein frames at the quantum level for the flat FRW
model. Obtained expressions for wave packet matched exactly in both the frames
indicating the equivalence of frames. We also showed that equivalence holds
true for various anisotropic quantum cosmological models, i.e., Bianchi I, V,
X, LRS Bianchi-I and Kantowski-Sachs models.
