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We compare the model power spectrum, computed based on perturbation theory(PT) with the power spectrum of luminous red galaxies (LRG) measured from theSDSSDR7 catalog, assuming a flat, CDM-dominated cosmology. The model includesthe effects of massive neutrinos, nonlinear matter clustering and nonlinear,scale-dependent galaxy bias in a self-consistent manner. We first test theaccuracy of PT-model by comparing the model predictions with the halo powerspectrum in real- and redshift-space measured from simulations without massiveneutrinos. We show that the PT-model with bias parameters being properlyadjusted can fairly well reproduce the simulation results. As a result thebest-fit parameters obtained from the hypothetical parameter fitting recover,within statistical uncertainties, the input cosmological parameters insimulations, including an upper bound on neutrino mass, if the power spectruminformation up to k~0.15h/Mpc is used. However, for the redshift-space powerspectrum, the best-fit cosmological parameters show a sizable bias from theinput values if using the information up to k~0.2h/Mpc, probably due tononlinear redshift distortion effect. Given these tests, we decided, as aconservative choice, to use the LRG power spectrum up to k=0.1h/Mpc in order tominimize possible unknown nonlinearity effects. In combination with the recentresults from Wilkinson Microwave Background Anisotropy Probe (WMAP), we derivea robust upper-bound on the sum of neutrino masses, given as m_nu,tot < 0.81eV(95% C.L.), marginalized over other parameters including nonlinear biasparameters and dark energy equation of state parameter. The neutrino mass limitis improved by a factor of 1.85 compared to the limit from the WMAP5 alone,m_nu,tot < 1.5eV.

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