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 5-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 $\sum _{}^{}{m}_{\nu }<0.28\mathrm{eV}$ at the 95% confidence level for a $\Lambda \mathrm{CDM}+m_{\nu }$ model, with a ${\sigma }_8$ equal to ${\sigma }_8=0.759\pm 0.025$ ($1\sigma$). When we allow the dark energy equation-of-state parameter $w$ to vary, we find $w=-1.30\pm 0.19$ for a general $w\mathrm{CDM}+m_{\nu }$ model with the 95% confidence level upper limit on the neutrino masses at $\sum _{}^{}{m}_{\nu }<0.59\mathrm{eV}$. The constraint on the dark energy equation of state further improves to $w=-1.125\pm 0.092$ when using also ACBAR and supernovae Union data, in addition to above, with a prior on the Hubble constant from the Hubble Space Telescope.

Figure 1

The conditional probability distribution $P(M;L,z)$ relating the galaxy luminosity $L$ and halo mass $M$, at different redshifts, as calculated in Refs. 16, 27 for SDSS at $z\sim 0.05$, DEEP2 at $z\sim 1$, and LBGs at $z\sim 4$. The probabilities to find a galaxy at a given luminosity in a halo of mass $M$ at redshift $z$ is plotted as a function of the halo mass for luminosity values for which we have galaxy bias data. In each of the distributions, the peak at low halo masses is related to galaxies of the given luminosity that appear as central galaxies, while the tail extending to higher masses is for galaxies that appear as satellites in more massive halos. The width of the central peak is related to the scatter in the relation between luminosity of central galaxies and halo mass and cannot simply be described by a delta function relating a one-to-one correspondence between mass and luminosity [19, 20, 21].

Figure 2

The galaxy bias-luminosity data set used in our analysis for the three average redshifts of SDSS ($z\sim 0.05$), DEEP2 ($z\sim 1$), and LBG ($z\sim 3.8$) in comparison with the bias prediction calculated for the best fit $\Lambda \mathrm{CDM}$ model. The x-axis magnitude values plotted are $M_r$ for SDSS, $M_B$ for DEEP2, and $M_{\mathrm{UV}}$ for LBGs at $z\sim 3.8$.

Figure 3

Constraints on the parameters of the $\Lambda \mathrm{CDM}+m_{\nu }$ model from WMAP alone (thin dark line), $\mathrm{WMAP}+\mathrm{LRG}+\mathrm{\text{bias}}$ data set at $z=0.05$ (thin light line) and $\mathrm{WMAP}+\mathrm{LRG}+\mathrm{\text{all bias}}$ data sets (bold line).

Figure 4

Joint two-dimensional posterior probability contour plot in the ${\sigma }_8\mathrm{\text{−}}{n}_s$ plane showing 68% and 95% contours from WMAP alone (contours behind) and $\mathrm{WMAP}+\mathrm{LRG}+\mathrm{\text{bias}}$ data at all redshifts (front contours).

Figure 5

Joint two-dimensional posterior probability contour plot in the ${\sigma }_8\mathrm{\text{−}}\sum _{}^{}{m}_{\nu }$ plane showing 68% and 95% contours from $\mathrm{WMAP}+\mathrm{LRG}+\mathrm{\text{bias}}$ data at all redshifts.

Figure 6

Joint two-dimensional posterior probability contour plot in the $\sum _{}^{}{m}_{\nu }\mathrm{\text{−}}w$ plane showing 68% and 95% contours from $\mathrm{WMAP}+\mathrm{LRG}$ and bias data at all redshifts (contours behind) and $\mathrm{WMAP}+\mathrm{ACBAR}+\mathrm{SNe}+\mathrm{LRG}+\mathrm{HST}$ and bias data at all redshifts (front contours).