\"Uber-Gravity and the Cosmological Constant Problem

Recently, the idea of taking ensemble average over gravity models has been introduced. Based on this idea, we study the ensemble average over (effectively) all the gravity models (constructed from Ricci scalar) dubbing the name \"uber-gravity which is a {\it{fixed point}} in the model space. The \"uber-gravity has interesting universal properties, independent from the choice of basis: $i)$ it mimics Einstein-Hilbert gravity for high-curvature regime, $ii)$ it predicts stronger gravitational force for an intermediate-curvature regime, $iii)$ surprisingly, for low-curvature regime, i.e. $R<R_0$ where $R$ is Ricci scalar and $R_0$ is a given scale, the Lagrangian vanishes automatically and $iiii)$ there is a sharp transition between low- and intermediate-curvature regimes at $R=R_0$. We show that the \"uber-gravity response is robust to all values of vacuum energy, $\rho_{vac}$ when there is no other matter. So as a toy model, \"uber-gravity, gives a way to think about the hierarchy problems e.g. the cosmological constant problem. Due to the transition at $R=R_0$ there is a chance for \"uber-gravity to bypass Weinberg's no-go theorem. The cosmology of this model is also promising because of its non-trivial predictions for small curvature scales in comparison to $\Lambda$CDM model.