Backreaction and the Role of Spatial Curvature in the Cosmic Neighborhood

Abstract We present the first direct computation of spatially averaged dynamical quantities in the local Universe, employing the Cosmicflows-4++ reconstruction and a covariant scalar averaging formalism. We extract the domain-averaged density, expansion rate, spatial curvature, and kinematical backreaction over cosmologically relevant domains around our Galaxy, extending up to a comoving radius of 300 Mpc h −1 . The resulting domain-averaged present-day energy budget features nontrivial variations with scale that reflect a nested structure within the cosmic neighborhood, including a large-scale void shell encompassing the local cosmic web. Remarkably, we find significant contributions to this energy budget from the average spatial curvature at the O ( 10 % ) level on all probed scales. By contrast, the kinematical backreaction remains much smaller throughout the surveyed volume, reaching at most a O ( 1 % ) contribution on the smallest scales considered, i.e., 30 Mpc h −1 . Convergence to the global ΛCDM background is not observed within this range of scales.