Ensemble Average Theory of Gravity

TL;DR

This paper proposes a unified gravity model combining various theories, favoring general relativity in high-curvature regions and predicting distinctive behaviors at different scales, including weaker or stronger gravity than GR.

Contribution

It introduces a novel ensemble average approach over gravity models leading to a specific stable $f(R,G)$ model with unique scale-dependent gravitational behavior.

Findings

Model aligns with local gravity tests in high-curvature regimes.

Predicts weaker gravity at large scales, implying a repulsive fifth force.

Shows stronger gravity at intermediate curvatures, distinguishable from $\\Lambda$CDM.

Abstract

We put forward the idea that all the theoretically consistent models of gravity have contributions to the observed gravity interaction. In this formulation, each model comes with its own Euclidean path-integral weight where general relativity (GR) has automatically the maximum weight in high-curvature regions. We employ this idea in the framework of Lovelock models and show that in four dimensions the result is a specific form of the $f(R,G)$ model. This specific $f(R,G)$ satisfies the stability conditions and possesses self-accelerating solutions. Our model is consistent with the local tests of gravity since its behavior is the same as in GR for the high-curvature regime. In the low-curvature regime the gravitational force is weaker than in GR, which can be interpreted as the existence of a repulsive fifth force for very large scales. Interestingly, there is an intermediate-curvature regime where the gravitational force is stronger in our model compared to GR. The different behavior of our model in comparison with GR in both low- and intermediate-curvature regimes makes it observationally distinguishable from $\Lambda$CDM.