4D scale-dependent Schwarzschild-AdS/dS black holes: study of shadow and weak deflection angle and greybody bounding

We investigate the shadow, deflection angle, and greybody bounding of a Schwarzschild-AdS/dS black hole in scale-dependent gravity. used EHT data to constrain parameter $\epsilon$. have found that within $1\sigma$ level uncertainty, $\epsilon M_0$ ranges at $10^{-11} - 10^{-16}$ orders magnitude for Sgr. A*, 10^{-17}$ M87*. Using these parameters, we explored how shadow radius behaves as perceived by static observer. known parameters A* M87*, different cast behavior near cosmological horizon even if same scaling were used. angle $\hat{\alpha}$ weak field limit both massive null particles, addition effect finite distances using non-asymptotically flat version Gauss-Bonnet theorem. strongly depends on particles. Tests $\epsilon$'s is only along points low impact parameters. For scaled BH AdS type can be tested high expense very value $\hat{\alpha}$. study rigorous bound factor scalar emitted from holes theory show transmission probability. The effects gravity factors are investigated, results indicate this case less than Schwarzschild hole.