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

Abstract

We propose a cosmological model, ü$\Lambda$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) $\Lambda$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$\Lambda$CDM. This yields $H_0=70.6_{-1.3}^{+1.1}$ km/s/Mpc, ${\Omega }_m=0.2861\pm 0.0092$ 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-$\alpha$ forest in quasar spectra, we get $\Delta {\chi }^2=-2.14$, where the best fit occurs at $H_0=71.2_{-1.5}^{+1.8}$ km/s/Mpc, ${\Omega }_m=0.280\pm 0.013$ and $z_{\oplus }=0.41_{-0.29}^{+0.31}$. Therefore, ü$\Lambda$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$\Lambda$CDM which points to interesting potential {\it smoking guns} in the observations of large scales structure at $z<z_{\oplus }$.

10 pages, 10 figures. CMB data has been added. Title has been changed. This version is compatible with the published one in PRD. Comments are welcome

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