An improved limit on the neutrino mass with CMB and redshift-dependent halo bias-mass relations from SDSS, DEEP2, and Lyman-Break Galaxies

We use measurements of luminosity-dependent galaxy bias at several different redshifts, SDSS at $z=0.05$, DEEP2 at $z=1$ and LBGs at $z=3.8$, combined with WMAP five-year cosmic microwave background anisotropy data and SDSS Red Luminous Galaxy survey three-dimensional clustering power spectrum to put constraints on cosmological parameters. Fitting this combined dataset, we show that the luminosity-dependent bias data that probe the relation between halo bias and halo mass and its redshift evolution are very sensitive to sum of the neutrino masses: in particular we obtain the upper limit of $\sum m_{\nu}<0.28$eV at the 95% confidence level for a $\Lambda CDM + m_{\nu}$ model, with a $\sigma_8$ equal to $\sigma_8=0.759\pm0.025$ (1$\sigma$). When we allow the dark energy equation of state parameter $w$ to vary we find $w=-1.30\pm0.19$ for a general $wCDM+m_{\nu}$ model with the 95% confidence level upper limit on the neutrino masses at $\sum m_{\nu}<0.59$eV. The constraint on the dark energy equation of state further improves to $w=-1.125\pm0.092$ when using also ACBAR and supernovae Union data, in addition to above, with a prior on the Hubble constant from the Hubble Space Telescope.