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 w(DE) 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 H-0. Taking into account the background expansion history as well as the evolution of matter perturbations delta(m), 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 delta(m). Using a higher value of H-0 derived from its direct measurement (H-0 greater than or similar to 70 km s(-1) Mpc(-1)) the data strongly support the nonlocal massive gravity model (-1.1 less than or similar to w(DE) less than or similar to -1.04 in the past) over the ACDM model (w(DE) = -1), whereas for a lower prior (67 km s(-1) Mpc(-1) less than or similar to H-0 less than or similar to 70 km s(-1) Mpc(-1)) the two models are statistically comparable.