Multiscale Cosmic Curvature: from Local Structures to Cosmology

This study tackles the impact Dark Energy (DE) in different systems by a simple unifying formalism. We introduce a parameter space that compare gravity across all cosmic scales, using the McVittie spacetime (McV) and connects spherically symmetric solutions with cosmological solutions. By analyzing the 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 the Kretschmann scalar of galaxy groups and clusters in their turnaround is $2{\mathrm{\Lambda }}^2$ which is three times the Kretschmann scalar of the Cosmological Consonant. This quantifies the DE domination in local structures.