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

TL;DR

This work investigates how 4D Einstein-Gauss-Bonnet gravity combined with Kaniadakis holographic dark energy influences black hole shadows within a cosmological background. Using Markov Chain Monte Carlo fits to Cosmic Chronometers and Type Ia supernovae, the authors constrain the model parameters, finding a phantom-like equation of state with $c\approx0.70$ and an EGB coupling $\alpha$ near GR with $\alpha\approx0.15$ while allowing a small negative lower bound for stability. They model black hole mass evolution under KHDE accretion (with an effective constant $A$) and compute the shadow's redshift evolution, revealing a vacuum-horizon hump tied to phantom crossing that is largely masked by dispersive plasma, though a residual $\sim$1–1.5% intrinsic deviation persists up to $z\approx2.5$. The study suggests that stacking shadow measurements across redshift bins could reveal this subtle dynamical dark energy signature in the strong-gravity regime, providing a potential observational probe of cosmology with EHT-like data.

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.

Figures (6)

• Figure 1: Confidence contours ($68\%$ and $95\%$) and 1D posterior distributions for the model parameters ($H_0, \Omega_{m0}, \alpha, \beta, c$) obtained from the joint analysis of CC + SNIa data. The grey dashed lines indicate the posterior means.
• Figure 2: The Hubble parameter $H(z)$ as a function of redshift. The blue solid line represents the best-fit KHDE model ($H_0=73.6, c=0.70, \alpha=0.146$), demonstrating strong agreement with the Cosmic Chronometers data (black dots).
• Figure 3: Evolution of the dark energy equation of state $w_{DE}(z)$. The horizontal dotted line represents the Phantom Divide ($w=-1$). All KHDE models exhibit a dynamical crossing: a phantom phase ($w < -1$) at low redshifts ($z \lesssim 0.25$) and a quintessence phase ($w > -1$) at higher redshifts.
• Figure 4: Evolution of the normalized black hole mass $M(z)/M_0$. The curves exhibit a non-monotonic behavior mirroring the EoS dynamics: mass increases with redshift in the local phantom regime ($z \lesssim 0.25$) due to negative accretion, and decreases in the high-redshift quintessence regime.
• Figure 5: Evolution of the black hole shadow radius in an optical vacuum ($n=1$) for the seven physical scenarios. The black dotted line represents the standard $\Lambda$CDM prediction. The colored curves exhibit a non-monotonic "hump" shape---rising at low redshifts ($z \lesssim 0.25$) and falling at high redshifts ($z > 0.25$)---which mirrors the mass evolution driven by the phantom-divide crossing. The vertical stratification is governed by the EGB coupling $\alpha$.