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

TL;DR

This paper derives exact solutions for an anisotropic Bianchi type I cosmological model with power-law scalar potentials in a generalized Saez-Ballester theory, highlighting implications for various dark energy scenarios.

Contribution

It introduces a new class of exact solutions with power-law scalar potentials in a generalized Saez-Ballester-like framework, connecting to quintessence, quintom, and phantom models.

Findings

Exact solutions are obtained for different dark energy regimes.

The volume function matches that of exponential potentials in multifield cosmology.

Scalar fields remain active throughout cosmic evolution.

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.