Barrow Holographic Dark Energy within Saez-Ballester Scalar Field and Lyra Geometry

This paper investigates the dynamical behavior of hypersurface homogeneous spacetime cosmological models within the framework of the scalar-tensor theory of gravitation formulated by Saez and Ballester (Phys. Lett. A, 113, 467 1986) in Lyra geometry. We present two cosmological models derived from this theory by solving the field equations using: (i) Special law of variation for Hubble’s parameter and (ii) the proportional relationship between the shear scalar σ2 and scalar expansion θ as described by Collins et al. (Gen. Rel. Grav. 12, 805 1980). For each model, we evaluate key dynamical parameters, including the equation of state (EoS) parameter, the deceleration parameter, the statefinder parameter, and the total energy density parameter of dark energy. Additionally, we determine the scalar field in both models. Our findings indicate that these models describe an accelerated expansion of the universe, with theoretical results showing reasonable agreement with observational data.