Bianchi type-I cosmological model in Sáez-Ballester theory with variable deceleration parameter

The present study is outcome of investigation of Bianchi type-I cosmological model in Saez-Ballester theory of gravity with variable deceleration parameter. Here, we have also considered variable cosmological constant $\Lambda$ which may be a probable candidate to discuss dark energy. The solution of the field equations has been found using variable deceleration parameter i.e. $q=-1+\beta H$ (with $\beta$ as a positive constant and $H$ as Hubble parameter) (Tiwari et al. in Eur. Phys. J. Plus 132:1–9, 2017) and suitable assumption of variable form of cosmological constant. We have expressed cosmological parameters such as Hubble parameter, deceleration parameter, energy density, pressure, cosmological constant and equation of state (EoS) in terms of redshift parameter and presented their dynamical behaviour graphically. In addition to Hubble parameter and deceleration parameter, the redshift variation of other higher order cosmographic parameters such as jerk, snap and lerk parameters has also been observed. The evolution of $(s,r)$ and $(q,r)$ trajectories has been examined to study different phases of the universe. Inspired by the study carried by Magana et al. (Mon. Not. R. Astron. Soc. 476(1), 1036, 2018), which consists of updated compilation of 51 points of homogenized and model-independent observational Hubble data, we have decided to use the same data for proposed study related with the expansion of the universe. Using these 51 values of observed Hubble measurements and performing $\chi^{2}$ test, we have found the best suitable value of model parameter $\beta$ and $H_{0}$ (present value of Hubble parameter). The authors have noted that the obtained outcomes coincide with the modern cosmological observational data.