Cosmological perturbations and observational constraints on nonlocal massive gravity

Nonlocal massive gravity can provide an interesting explanation for the late-time cosmic acceleration, with a dark energy equation of state wDE smaller than -1 in the past. We derive the equations of linear cosmological perturbations to confront such models with the observations of large-scale structures. The effective gravitational coupling to nonrelativistic matter associated with galaxy clusterings is close to Newton's gravitational constant G for a mass scale m slightly smaller than today's Hubble parameter H₀. Taking into account the background expansion history as well as the evolution of matter perturbations δₘ, we test for these models with Type Ia Supernovae (SnIa) from Union 2.1, the cosmic microwave background (CMB) measurements from Planck, a collection of baryon acoustic oscillations (BAO), and the growth rate data of δₘ. Using a higher value of H₀ derived from its direct measurement (H₀70 km s^-1 Mpc^-1) the data strongly support the nonlocal massive gravity model (-1.1wDE-1.04 in the past) over the ΛCDM model (wDE=-1), whereas for a lower prior ($67 km {s}^{{-}1} {Mpc}^{{-}1}{}{H}₀{}70 km {s}^{{-}1} {Mpc}^{{-}1}$) the two models are statistically comparable.