\"Uber-Gravity and the Cosmological Constant Problem

TL;DR

This paper introduces 'uber-gravity', an ensemble-averaged model of gravity that exhibits universal properties, transitions at a specific curvature scale, and potential implications for the cosmological constant problem and cosmology.

Contribution

It proposes a novel ensemble average over Ricci scalar-based gravity models, revealing a fixed point model with unique universal properties and potential to address hierarchy and cosmological constant problems.

Findings

Mimics Einstein-Hilbert gravity at high curvature

Predicts stronger gravity at intermediate curvature

Vanishes at low curvature, enabling a transition at R=R_0

Abstract

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.