Emerging spatial curvature can resolve the tension between high-redshift CMB and low-redshift distance ladder measurements of the Hubble constant

Abstract: The measurements of the Hubble constant reveal a tension between high-redshift (CMB) and low-redshift (distance ladder) constraints. So far neither observational systematics nor new physics has been successfully implemented to explain this tension away. This paper present a new solution to the Hubble constant problem. The solution is based on the Simsilun simulation (relativistic simulation of the large scale structure of the Universe) with the ray-tracing algorithm implemented. The initial conditions for the Simsilun simulation were set up as perturbations around the $\Lambda$CDM model. However, unlike in the Standard Cosmological Model (i.e. $\Lambda$CDM model + perturbations), within the Simsilun simulation relativistic and nonlinear evolution of cosmic structures leads to the phenomenon of emerging spatial curvature, where the mean spatial curvature evolves from spatial flatness of the early universe towards slightly curved present-day universe. Consqeuently, the present-day expansion rate is slightly faster compared to the spatially flat $\Lambda$CDM model. The results of the ray-tracing analysis show that the universe which starts with initial conditions consistent with the Planck constraints should have the Hubble constant $H_0 = 72.5 \pm 2.1$ km s$^{-1}$ Mpc$^{-1}$. When the Simsilun simulation was re-run with no inhomogeneities imposed, the Hubble constant inferred within such a homogeneous simulation was $H_0 = 68.1 \pm 2.0$ km s$^{-1}$ Mpc$^{-1}$. Thus, the inclusion of nonlinear relativistic evolution that leads to the emergence of the spatial curvature can explain why the low-redshift measurements favour higher values compared to high-redshift constraints and alleviate the tension between the CMB and distance ladder measurements of the Hubble constant.