Cosmological Constraints on 4D Einstein-Gauss-Bonnet Gravity and Kaniadakis Holographic Dark Energy: Implications for Black Hole Shadows

Abstract: The direct imaging of black holes by the Event Horizon Telescope (EHT) enables precision tests of gravity in the strong-field regime. We investigate the cosmological evolution and optical appearance of black holes in 4D Einstein-Gauss-Bonnet (EGB) gravity coupled with Kaniadakis Holographic Dark Energy (KHDE). Utilizing Cosmic Chronometers (CC) and Type Ia Supernovae (SNIa) datasets, we constrain model parameters via Markov Chain Monte Carlo (MCMC) analysis. Results indicate that the late-time universe statistically favors a phantom-like equation of state ($c \approx 0.704$). Regarding the EGB coupling $α$, although data favor a positive value, the parameter space permits negative values down to a theoretical stability cut-off at $α\approx -0.03$. While the best-fit suggests deviation, results remain consistent with General Relativity ($α=0$) within the $2σ$ confidence level. Based on these constraints, we model the secular mass accretion history (treating accretion efficiency as a phenomenological constant) and compute the shadow radius evolution. We find that in a realistic dispersive plasma environment, refractive effects significantly mask intrinsic gravitational and dark energy signatures, causing global shadow shrinkage. Nevertheless, a characteristic systematic intrinsic deviation of $\sim 1\%$--$1.5\%$ (under a conservative accretion scenario) persists at redshifts $z \lesssim 1.5$ relative to standard $Λ$CDM predictions. These findings suggest that despite environmental dominance, precise statistical analyses of shadow populations could disentangle these subtle dynamic dark energy signals from the standard cosmological paradigm.