Cosmic acceleration & deceleration with f(R,T) gravity

This study includes the cosmic evolution and the potential periodicity of the universe. It employs a periodic varying deceleration parameter (PVDP) within the framework of f(R,T) theory of gravity, with a specific focus on the Bianchi-II model. We explore the dynamic nature of the universe, with physical and geometrical properties within this theoretical framework. We have also analyzed the cosmographic parameters, including jerk, snap, and lerk, for deeper insights into the universe's evolution and behavior. Utilizing state finder diagrams and the Om diagnostic (which illustrates the variation of Om(z) with redshift) signifying a shift from matter dominance to a stronger influence of dark energy (DE), we construct a comprehensive map of the universe's trajectory and behavior. By employing the Bianchi-II model within the f(R,T) theory, our proposed model helps us in understanding the universe's oscillatory patterns and underlying mechanisms. This research significantly contributes to our understanding of cosmic evolution and periodicity within the f(R,T) theory.