Neutrino mass constraint from the Sloan Digital Sky Survey power spectrum of luminous red galaxies and perturbation theory

We compare the model power spectrum, computed based on perturbation theory, with the power spectrum of luminous red galaxies (LRG) measured from the Sloan Digital Sky Survey Data Release 7 catalog, assuming a flat, cold dark matter-dominated cosmology. The model includes the effects of massive neutrinos, nonlinear matter clustering and nonlinear, scale-dependent galaxy bias in a self-consistent manner. We first test the accuracy of the perturbation theory model by comparing the model predictions with the halo power spectrum in real-and redshift-space, measured from 70 simulation realizations for a cold dark matter model without massive neutrinos. We show that the perturbation theory model with bias parameters being properly adjusted can fairly well reproduce the simulation results. As a result, the best-fit parameters obtained from the hypothetical parameter fitting recover, within statistical uncertainties, the input cosmological parameters in simulations, including an upper bound on neutrino mass, if the power spectrum information up to k similar or equal to 0: 15 hMpc(-1) is used. However, for the redshift-space power spectrum, the best-fit cosmological parameters show a sizable bias from the input values if using the information up to k similar or equal to 0: 2 hMpc(-1), probably due to nonlinear redshift distortion effect. Given these tests, we decided, as a conservative choice, to use the LRG power spectrum up to k similar or equal to 0.1 hMpc(-1) in order to minimize possible unknown nonlinearity effects. In combination with the recent results from Wilkinson Microwave Background Anisotropy Probe (WMAP), we derive a robust upper bound on the sum of neutrino masses, given as Sigma m(nu) <= 0: 81 eV (95% C. L.), marginalized over other parameters including nonlinear bias parameters and dark energy equation of state parameter. The upper bound is only slightly improved to Sigma m(nu) <= 0: 80 eV if including the LRG spectrum up to k = 0.2 hMpc(-1), due to severe parameter degeneracies, although the constraint may be biased as discussed above. The neutrino mass limit is improved by a factor of 1.85 compared to the limit from the WMAP5 alone, Sigma m(nu) <= 1: 5 eV.