Abstract: We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in three models possessing the Big-Rip Singularity : the model mainly based on tachyon field and pseudo-tachyon field with respect to the pseudo-space RI ( iR , where ‘R’ is the scale factor of the universe and i 1 ). It was shown that in the pseudo-tachyon model the Hamiltonian is well defined and hence wave function of the universe is not obliged to vanish at the values of the variables, corresponding to the scale factor RI of the appearance of the Big-Rip singularity. There is some kind of a classical-quantum correspondences in the classical cosmological tachyon model exists an infinite oneparameter set of the cosmological evolutions encountering and crossing the Big-Rip singularity. In all other cases—mainly the Big-Brake and Big-Bang singularity in the scalar field model and the Big-Crunch and the Big-Rip singularities in both the tachyon and pseudo tachyon field model we have observed the phenomenon of the quantum avoidance of singularities. It corresponds to the degeneration of the corresponding cosmological trajectories in classical theory. It was shown that a negative pressure may be acquired from Big-Rip Singularity, which is responsible for the Big-Bang singularity and then the expansion of the universe. Again we study the Hamiltonian formalism for a massive scalar field and particle production with the Gaussian group of energy SU(6), a new type of energy source called latent energy group from the past infinity of the space-like hyper surface and study the de-Sitter Space which assumed with a complex space-time of the scale factor R+iRI , where the scale factor R stands for 4-dimensional space time and (iRI), the internal space of D-dimensions, i.e., we consider dS-space as (4+D) dimensions with scale factor I R iR . It is compared with Kaluza-Klein Cosmology of (4+D) dimensions