Emergence of spatial curvature

Abstract

This paper investigates the phenomenon of emergence of spatial curvature. This phenomenon is absent in the Standard Cosmological Model, which has a flat and fixed spatial curvature (small perturbations are considered in the Standard Cosmological Model but their global average vanishes, leading to spatial flatness at all times). This paper shows that with the nonlinear growth of cosmic structures the global average deviates from zero. The analysis is based on the {\em silent universes} (a wide class of inhomogeneous cosmological solutions of the Einstein equations). The initial conditions are set in the early universe as perturbations around the $\Lambda$CDM model with $\Omega_m = 0.31$, $\Omega_\Lambda = 0.69$, and $H_0 = 67.8$ km s$^{-1}$ Mpc$^{-1}$. As the growth of structures becomes nonlinear, the model deviates from the $\Lambda$CDM model, and at the present instant if averaged over a domain ${\cal D}$ with volume $V = (2150\,{\rm Mpc})^3$ (at these scales the cosmic variance is negligibly small) gives: $\Omega_m^{\cal D} = 0.22$, $\Omega_\Lambda^{\cal D} = 0.61$, $\Omega_{\cal R}^{\cal D} = 0.15$ (in the FLRW limit $\Omega_{\cal R}^{\cal D} \to \Omega_k$), and $\langle H \rangle_{\cal D} = 72.2$ km s$^{-1}$ Mpc$^{-1}$. Given the fact that low-redshift observations favor higher values of the Hubble constant and lower values of matter density, compared to the CMB constraints, the emergence of the spatial curvature in the low-redshift universe could be a possible solution to these discrepancies.