Quantum Bianchi Type IX Cosmology in K-Essence Theory

We use one of the simplest forms of the K-essence theory and apply it to the anisotropic Bianchi type IX cosmological model, with a barotropic perfect fluid modeling the usual matter content. We show that the most important contribution of the scalar field occurs during a stiff matter phase. Also, we present a canonical quantization procedure of the theory which can be simplified by reinterpreting the scalar field as an exotic part of the total matter content. The solutions to the Wheeler-DeWitt equation were found using the Bohmian formulation Bohm (Phys. Rev. 85(2):166, 1952) of quantum mechanics, employing the amplitude-real-phase approach Moncrief and Ryan (Phys. Rev. D 44:2375, 1991), where the ansatz for the wave function is of the form Ψ(? ^μ )=χ(?)W(? ^μ ) \(e^{- S(\ell ^{\mu })},\) , where S is the superpotential function, which plays an important role in solving the Hamilton-Jacobi equation.