Massive gravity at short distances

Postulating that the graviton has a tiny mass would naturally explain possible deviations from general relativity at cosmological scales, in particular providing a good candidate for dark energy. While being a well-defined effective field theory at astrophysical and cosmological distances, an uncomfortable feature of massive gravity is that it becomes quantum-mechanically strongly coupled below a macroscopic scale of order 1000 km. I will discuss why it has been hard to find a traditional Higgs mechanism for the theory below this distance scale and argue in favour of a particular short-distance completion, hinted by the gauge/gravity correspondence.