Bouncing and Coasting Universe with Exact Quantum-Classical Correspondence

When the scale factor of expansion universe is written as $ a(t)\equiv Ae^{\alpha(t)}$, with $A$ some real constant and $\alpha(t)$ a function, gravitational action $I_G$ appears in same form matter $I_M$ for homogeneous isotropic scalar field specific factor-dependent potential. We observe that by making analytic continuation Lagrangian function this to complex plane $\alpha$, one can obtain terms corresponding both parts total describes viable cosmological model. The solution gives bouncing coasting universe, which first contracts then expands linearly, smooth bounce between them. Such bounce, called Tolman wormhole, due Casimir-like negative energy naturally solution. In novel approach quantum cosmology, we perform canonical quantization above model using operator method show it circumvent ordering ambiguity conventional formalism. It leads wave equation solving get interesting result ground state nonzero energy. This different from Wheeler-DeWitt possesses exact quantum-classical correspondence during all epochs.