Ensemble Average Theory of Gravity
  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.
