Neutrino mass constraint with 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
(PT) with the power spectrum of luminous red galaxies (LRG) measured from the
SDSSDR7 catalog, assuming a flat, CDM-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 PT-model by comparing the model predictions with the halo power
spectrum in real- and redshift-space measured from simulations without massive
neutrinos. We show that the PT-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~0.15h/Mpc 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~0.2h/Mpc, 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=0.1h/Mpc 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 m_nu,tot < 0.81eV
(95% C.L.), marginalized over other parameters including nonlinear bias
parameters and dark energy equation of state parameter. The neutrino mass limit
is improved by a factor of 1.85 compared to the limit from the WMAP5 alone,
m_nu,tot < 1.5eV.
