Fractal Gravity and Bianchi Type-VI Cosmology: Constraints and Observational Viability

In this study, we investigate anisotropic Bianchi Type VI cosmological model within the framework of fractal universe. By utilizing the energy-momentum tensor for a perfect fluid, we solved the corresponding field equations. In this study, we derive leading cosmological parameters, including the hubble parameter Formula: see text and deceleration parameter Formula: see text in terms of cosmic time and redshift also. To determine the model parameters such as Formula: see text, Formula: see text, and the hubble constant Formula: see text, the hubble dataset was analyzed using the Formula: see text test. This analysis reveals the best-fit values of Formula: see text, Formula: see textFormula: see text, Formula: see text, Formula: see text and RMSE = 11.4068 matching with the Formula: see textCDM model. We carry blow by blow analysis of the model’s characteristics via energy density Formula: see text, pressure Formula: see text and EoS parameter. We examine whether the energy conditions NEC (null energy condition), SEC (strong energy condition), WEC (weak energy condition), and DEC (dominant energy condition) are satisfied. Furthermore, the diagnostic parameters are analyzed to evaluate the deviation of the obtained model from the Formula: see text CDM model and to classify various dark energy models during the universe’s expansion. The om diagnostic is depicted as a function of redshift for Formula: see text and Formula: see text reveals that Formula: see text settles around Formula: see text with slight deviation in the range Formula: see text. The model closely aligns with Formula: see textCDM at higher redshifts. The pair of statefinder diagnostics Formula: see text vs. Formula: see text is also discussed, and our model for Formula: see text represents the Formula: see textCDM model.