Matter power spectra in viable f(R) gravity models with massive neutrinos

We investigate the matter power spectra in the power law and exponential types of viable f(R) theories along with massive neutrinos. The enhancement of the matter power spectrum is found to be a generic feature in these models. In particular, we show that in the former type, such as the Starobinsky model, the spectrum is magnified much larger than the latter one, such as the exponential model. A greater scale of the total neutrino mass, Sigma m(v) is allowed in the viable f (R) models than that in the ACDM one. We obtain the constraints on the neutrino masses by using the CosmoMC package with the modified MGCAMB. Explicitly, we get Sigma m(v) > m(v) < 0.451 (0.214) eV at 95% C.L. in the Starobinsky (exponential) model, while the corresponding one for the ACDM model is Sigma m(v) < 0.200 eV. Furthermore, by treating the effective number of neutrino species Neff as a free parameter along with Em(v), we find that N-eff = 3.78(0.84)(+0.64) (3.47(0.60)(+0.74)) and Sigma m(v) = 0.533(0.411)(+0.254) (<0.386) eV at 95% C.L. in the Starobinsky (exponential) model. (C) 2014 The Authors. Published by Elsevier B.V.