$H_0$ tension as a hint for a transition in gravitational theory

Abstract

We propose a cosmological model, ü$Λ$CDM, based on {\it über-gravity}, which is a canonical ensemble average of many theories of gravity. In this model, we have a sharp transition from (a purely) $Λ$CDM era to a phase in which the Ricci scalar is a constant. This transition occurs when the Ricci scalar reaches a critical scale or alternatively at a transition redshift, $z_\oplus$. We use the observations of baryonic acoustic oscillations (BAO) and Supernovae Ia (SNe), as well as the cosmic microwave background (CMB) data to constrain ü$Λ$CDM. This yields $H_0=70.6_{-1.3}^{+1.1}$ km/s/Mpc, $Ω_m=0.2861 \pm{0.0092} $ and $z_\oplus=0.537_{-0.375}^{+0.277}$, providing a marginally better fit with a Akaike information criterion of 0.8. %After adding in the data from BAO in the Lyman-$α$ forest in quasar spectra, we get $Δχ^2=-2.14$, where the best fit occurs at $H_0=71.2_{-1.5}^{+1.8}$ km/s/Mpc, $Ω_m=0.280\pm 0.013$ and $z_{\oplus}= 0.41^{+0.31}_{-0.29}$. Therefore, ü$Λ$CDM can ease the $H_0$-tension, albeit marginally, with one additional free parameter. We also provide a preliminary study of the linear perturbation theory in ü$Λ$CDM which points to interesting potential {\it smoking guns} in the observations of large scales structure at $z < z_{\oplus}$.

Figures (10)

• Figure 1: Blue line is our Lagrangian (\ref{['ubergravity-Lagrangian']}) for $\Lambda=0.32\,R_0$ and $\beta=2.5$ where we do sum up to $N=1000$ (It is easy to see that for larger $N$'s the plot is practically the same.) and yellow dashed line shows standard EH action with the same value for $\Lambda$.
• Figure 2: Blue line is the trace of equation of motion in über-gravity where $\Lambda=0.32\,R_0$, $\beta=2.5$ and yellow dashed line shows the same for the EH action. For $\rho > \rho_{{\rm \ddot{u}ber}}$ the matter field sees gravity as standard EH action and for $\rho < \rho_{{\rm \ddot{u}ber}}$ the gravity switches to $R=R_0$.
• Figure 3: Comparison of the base $\Lambda$CDM model with ü$\Lambda$CDM parameter constraints from data set Table \ref{['tab:data']}. It is obvious that ü$\Lambda$CDM prefers higher $H_0$ and less $\Omega_m$ in comparison with $\Lambda$CDM.
• Figure 4: The comparison of ü$\Lambda$CDM with base CMB temperature and polarization data (green contour plots) and CMB+BAO+R16 constrained (gray contour plots)
• Figure 5: A 3D plot of $\Omega_m$ versus the transition scale factor $a$ and Hubble parameter.