Observational constraints of diffusive dark-fluid cosmology

In this manuscript, we investigate late-time cosmology and the evolution of cosmic structures using an interacting dark fluid model in which dark matter (DM) and dark energy (DE) interact through a diffusive mechanism. To provide a comprehensive understanding, we derive the background evolution and perturbation equations within this model and obtain cosmological parameters through MCMC simulations. We use recent measurements for statistical analysis and constrain the parameters $H_0$ in km/s/Mpc, $\Omega_m$, $r_d$, $M$, $\sigma_8$, $S_8$, and the interaction term $Q_{dm}$. From the constrained values of $Q_{dm}$, we show that the diffusive model is a promising alternative DE model, capable of driving late-time cosmic acceleration due to energy exchange from DM to DE. State-finder diagnostics indicate that the model behaves like a Chaplygin gas when energy transfers from DM to DE during the Universe's expansion. We also investigate the growth of density contrast, finding $\delta_m(z)\gg\delta_{de}(z)$, which highlights the dominant role of DM in structure formation. Redshift space distortion and growth rate analysis show that minor deviations from $\Lambda$CDM at low redshifts, with larger differences at higher redshifts, indicate the impact of energy diffusion on early structure growth. Finally, we perform a detailed statistical analysis, including ${\mathcal{L}(\hat{\Theta}|data)}$, $\chi^2$, $\rm{AIC}$, and $\rm{BIC}$, which strongly supports the proposed diffusive dark-fluid model.