The Scale for the Expansion of the Universe: From Local Structures to Cosmology

This study tackles the impact dark energy in different systems by a simple unifying formalism. We introduce a parameter space to compare gravity tests across all cosmic scales, using the McVittie spacetime (MCV), that connect spherically symmetric solutions with cosmological solutions. By analyzing invariant scalars, the Ricci, Weyl, and Kretschmann scalars, we develop a phase-space description that predicts the dominance of the Cosmological Constant. We explore three cases: (1) the local Hubble flow around galaxy groups and clusters, (2) spherical density distributions and (3) binary motion. Our results show that galaxy groups and clusters exhibit Kretschmann scalar values consistent with the Cosmological Constant curvature, indicating where dark energy dominates.