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 solve the corresponding field equations. In this study, we derive leading cosmological parameters, including the hubble parameter H and deceleration parameter q in terms of cosmic time and redshift also. To determine the model parameters such as k, [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 text], [Formula: see text], [Formula: see text] and [Formula: see text] match with the [Formula: see text]CDM model. We carry blow-by-blow analysis of the model’s characteristics via energy density [Formula: see text], pressure p and EoS parameter. We examine whether the energy conditions — null energy condition (NEC), strong energy condition (SEC), weak energy condition (WEC) and dominant energy condition (DEC) — 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] revealing 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 text]CDM at higher redshifts. The pair of statefinder diagnostics r versus s is also discussed, and our model for [Formula: see text] represents the [Formula: see text]CDM model.