Power law scalar potential in the Saez-Ballester like theory: Exact solutions in the Bianchi type I case

Abstract

An anisotropic Bianchi type I cosmological model with power-law scalar-field potentials of the form $V(\psi_1,\psi_2)=V_1\psi_1^{\pm\lambda_1}+V_2\psi_2^{\pm\lambda_2}$ is studied within a generalized S\'aez--Ballester--K-essence-like theory involving standard kinetic terms and a mixed coupling contribution. In order to solve the corresponding field equations, for negative sign case, the mixed term introduces an essential constraint on the associated parameter, which yields relevant contributions to quintessence, quintom, and phantom scenarios in the context of primordial inflation. Exact solutions for these regimes are obtained through an appropriate change of variables. It is shown that the volume function of the universe derived from the present power-law scalar potential coincides with that obtained from exponential scalar potentials in standard chiral multifield cosmology, while the scalar fields remain dynamically present throughout the cosmic evolution.