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 $300~\mathrm{Mpc}/h$. 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 $\mathcal{O}(10\%)$ level on all probed scales. By contrast, the kinematical backreaction remains much smaller throughout the surveyed volume, reaching at most a $\mathcal{O}(1\%)$ contribution on the smallest scales considered, i.e., $30~\mathrm{Mpc}/h$. Convergence to the global $\Lambda$CDM background is not observed within this range of scales.