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, k1 and the hubble constant H0, the hubble dataset was analyzed using the R2 test. This analysis reveals the best-fit values of k=54.26−0.21+0.20, k1=−0.294−1.9+1.9, H0=70.22−1.05+1.05, R2=0.9280 and RMSE=11.4068 match with the ΛCDM model. We carry blow-by-blow analysis of the model’s characteristics via energy density ρ, 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 ΛCDM model and to classify various dark energy models during the universe’s expansion. The om diagnostic is depicted as a function of redshift for k=54.26 and k1=−0.294, revealing that Ω(z) settles around 0.3 with slight deviation in the range −0.25≤z≤0.25. The model closely aligns with ΛCDM at higher redshifts. The pair of statefinder diagnostics r versus s is also discussed, and our model for (r,s)=(1,0) represents the ΛCDM model. © 2026 World Scientific Publishing Company.