Classical and Quantum Exact Solutions for a FRW Multiscalar Field Cosmology with an Exponential Potential Driven Inflation

A flat Friedmann-Robertson-Walker (FRW) multiscalar field cosmology is studied with a particular potential of the form V(phi,sigma)=V(0)e(-lambda 1 phi-lambda 2 sigma), which emerges as a relation between the time derivatives of the scalars field momenta. Classically, by employing the Hamiltonian formalism of two scalar fields (phi,sigma) with standard kinetic energy, exact solutions are found for the Einstein-Klein-Gordon (EKG) system for different scenarios specified by the parameter lambda(2)=lambda(2)(1) + lambda(2)(2), as well as the c-folding function N-e which is also computed. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables.