We study the black hole's shadow for Schwarzschild - de Sitter and Kerr - de Sitter metrics with the contribution of the cosmological constant \Lambda. Based on the reported parameters of the M87* black hole shadow we obtain constraints for the $\Lambda$ and show the agreement with the cosmological data. It is shown that, the coupling of the \Lambda-term with the spin parameter reveals peculiarities for the photon spheres and hence for the shadows. Within the parametrized post-Newtonian formalism the constraint for the corresponding \Lambda-determined parameter is obtained.
Motivated by Hubble tension, we have recently witnessed a number of "model independent" $H_0$ determinations at cosmological scales. Here we compare two "model independent" techniques, Taylor expansion and Gaussian Processes (GP). While Taylor expansion is truly model independent in a limited range, we show that one can reduce the $H_0$ errors by increasing the range of the expansion, but the approximation suffers. For GP, we confirm for the Mat\'ern class kernels that the errors on $H_0$ decrease as the parameter $\nu \rightarrow \infty$, where we recover the Gaussian kernel. The errors from GP are typically smaller than Taylor and by mapping the GP analysis back into the Taylor expansion, we show that GP explores a smaller portion of the parameter space. In a direct comparison of GP with the CPL model, the simplest model of dynamical dark energy, we see that correlations are suppressed by GP relative to CPL. Therefore, GP cannot be model independent. We emphasise that if a truly model independent statement of Hubble tension exists, then it will have serious consequences for the FLRW framework.