Observational Constraints on Anisotropic Cosmology Through the Deceleration Parameter in Saez–Ballester Theory

We explore the cosmological tests of the deceleration parameter \(q=K-\gamma/H\), where \(K\) and \(\gamma\) are arbitrary constants in a Bianchi type-III cosmological model in the framework of the Saez–Ballester theory of gravitation. Under the assumption that the shear scalar (\(\sigma\)) is proportional to the expansion scalar (\(\theta\)), we evaluate the physical and kinematic parameters, the jerk parameter, and the deceleration parameter (DP) in the early deceleration phase \((q>0)\) and the current acceleration phase \((q<0)\). The energy conditions and the \(Om(z)\) analysis for our spatially homogeneous and anisotropic Bianchi type-III model are discussed in details. Furthermore, we perform a \(\chi^{2}\) test to obtain the best fit values of the model parameters in the derived model by using \(46\,H(z)\) data sets in the redshift range \(0\leq z\leq 2.36\) and also analyze the present age of the universe.