Bianchi Space-Time Metric-I in Landau and Lifshitz Energy Tensor, Including Linearly Varying Deceleration Parameter with Saez-Ballester Theory of Gravitation

In this study, the Bianchi Space Metric-I cosmological model is introduced within the context of the Saez-Ballester theory of gravitation, including the incorporation of scale factors in the framework of gravity. The objective is to derive an exact solution for the cosmological field equation, with consideration given to the Landau and Lifshitz energy tensor. This solution includes a metric potential comprising commoving vectors and an energy conservation equation. Within this framework, a set of relations between the deceleration parameter, Hubble parameter, and average scale factor is established. By adopting a probable set of relations, the influence of the dynamics of the deceleration parameter on energy density and isotropic pressure, particularly in exponential form, is explored. A key proposal involves the utilization of a linearly decelerating parameter alongside exponential scale factors. The results are presented graphically, offering insights into potential future cosmological models. These graphical representations are intended to facilitate the understanding of numerous physical and kinematical properties inherent in the cosmological model under investigation.