Massive graviton as a testable cold dark matter candidate

We construct a model of gravity where the tensor graviton mode is massive, while spatially flat cosmological solutions and linearized equations for scalar and vector metric perturbations are not modified. This model is free of the vDVZ discontinuity and strong coupling problem, has no ghosts and does not suffer from rapid classical instabilities. The mass of the graviton can be as large as (10^{15} cm)^{-1}, being constrained by the pulsar timing measurements. We argue that non-relativistic gravitational waves can comprise the cold dark matter and may be detected by the future gravitational wave searches. Our model also allows for the anthropic solution of the cosmological constant problem.