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

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 away this tension. This paper presents 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 $\mathrm{\Lambda }\mathrm{CDM}$ model. However, unlike in the standard cosmological model (i.e., $\mathrm{\Lambda }\mathrm{CDM}\mathrm{model}+\text{perturbations}$), within the Simsilun simulation relativistic and nonlinear evolution of cosmic structures lead to the phenomenon of emerging spatial curvature, where the mean spatial curvature evolves from the spatial flatness of the early Universe towards the slightly curved present-day Universe. Consequently, the present-day expansion rate is slightly faster compared to the spatially flat $\mathrm{\Lambda }\mathrm{CDM}$ 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 $H_0=72.5\pm 2.1\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. When the Simsilun simulation was rerun with no inhomogeneities imposed, the Hubble constant inferred within such a homogeneous simulation was $H_0=68.1\pm 2.0\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. Thus, the inclusion of nonlinear relativistic evolution that leads to the emergence of the spatial curvature can explain why the low-redshift measurements favor higher values compared to the high-redshift constraints and alleviate the tension between the CMB and distance ladder measurements of the Hubble constant.

Figure 1

Evolution of the global (mean) expansion rate (Upper panel) and the spatial curvature (Lower panel) within the Simsilun simulation. The initial conditions for the Simsilun simulation have been set up using density fluctuations from the Millennium simulation imposed on the Planck’s $\mathrm{\Lambda }\mathrm{CDM}$ model at $z_i=80$. As long as perturbations remain within the linear regime ($t<1\mathrm{Gyr}$) the mean evolution follows the $\mathrm{\Lambda }\mathrm{CDM}$ model. Once the system enters a nonlinear regime the spatial curvature emerges and the expansion rate slightly increases compared to the $\mathrm{\Lambda }\mathrm{CDM}$ model.

Figure 2

A single mock supernova catalog generated within the Simsilun simulation. 217 generated distance-redshift relations has been Gaussian scattered using uncertainties from the Union2.1 data set. Upper panel shows the luminosity distance $D_L$; middle panel shows distance residuals $\mathrm{\Delta }{D}_L$ from the best-fit distance-redshift relation (1); lower panel shows residuals in brightness $\mathrm{\Delta }\mu =5{\log }_{10}(1+\mathrm{\Delta }{D}_L/D_L)$.

Figure 3

The Hubble constant evaluated within the Simsilun simulation (red solid line). The constraints are inferred from the slope of the distance-redshift relation (21) and result with $H_0^{\mathrm{DL}}=72.5\pm 2.1\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. If the Simsilun simulation is run with no inhomogeneities imposed (i.e., the FLRW case) then the Hubble constant inferred from the slope of the distance-redshift is $H_0^{\mathrm{DL}}=68.1\pm 2.0\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ (purple dashed line). For comparison, the green dotted line (on the left) presents the Gaussian profile with the mean 67.81 and the standard deviation 0.92 (cf. CMB constraints [3]) and the blue dotted line (on the right) shows a Gaussian profile with a mean $73.24\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and a standard deviation $1.74\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ (cf. distance ladder constraints [2]).