Classical and quantum exact solutions for the anisotropic Bianchi type I in multi-scalar field cosmology with an exponential potential driven inflation

Abstract

The anisotropic Bianchi type I in multi-scalar field cosmology is studied with a particular potential of the form V=V0e−[λ1ϕ1+⋯+λnϕn], which emerges as a condition between the time derivatives of their corresponding momenta. Using the Hamiltonian formalism for the inflation epoch with a quintessence framework we find the exact solutions for the Einstein-Klein-Gordon (EKG) system with different scenarios specified by the parameter λ2=∑i=1nλi2. For the quantum scheme of this model, the corresponding Wheeler-DeWitt (WDW) equation is solved by applying an appropriate change of variables and suitable ansatz.