Although the Nobel Prize last year went for the accelerated expansion of the Universe, in fact acceleration is not a many-sigma result. What is a many-sigma result is that the expansion is not decelerating by as much as it should be given the mass density. This begs the question: Could gravity be weaker than expected on cosmological scales? Models with, say, an exponential cutoff of the gravitational force law at long distances are theoretically ugly (they are like massive graviton theories and usually associated with various pathologies) but as empirical objects they are nice: A model with an exponentially suppressed force law at large distance is predictive and simple.
The idea is to compute the detailed expansion history and linear growth factor (for structure formation) for a homogeneous and isotropic universe and compare to existing data. By how much is this ruled out relative to a cosmological-constant model? The answer may be
a lot but if it is only by a few sigma, then I think it would be an interesting straw-man. For one, it has the same number of free parameters (one length scale instead of one cosmological constant). For two, it would sharpen up the empirical basis for acceleration. For three, it would exercise an idea I would like to promote: Let's choose models on the joint basis of theoretical reasonableness and computability, not theoretical reasonableness alone! If we had spent the history of physics with theoretical niceness as our top priority, we would never have got the Bohr atom or quantum mechanics!
One amusing note is that if gravity does cut off at large scales, then in the very distant future, the Universe will evolve into an inhomogeneous fractal. Fractal-like inhomogeneity is something I have argued against for the present-day Universe.