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

TL;DR

The paper tackles tightening constraints on the sum of neutrino masses and the dark energy equation of state by exploiting the redshift evolution of galaxy bias within a halo-model framework. It links the observed luminosity-dependent bias $b_g(L,z)$ to the underlying halo bias $b_h(M,z)$ via a conditional luminosity function $P(M|L,z)$, and fits this to WMAP5, SDSS LRG, and multi-redshift bias data using a CosmoMC-based MCMC analysis. The main results show $\sum m_ν<0.28$ eV (95% CL) for $\Lambda$CDM+$m_ν$, with $\sigma_8=0.759\pm0.025$, and, when allowing $w$ to vary, $w=-1.30\pm0.19$ with $\sum m_ν<0.59$ eV; including additional priors (ACBAR, SNe, and an $H_0$ prior) tightens to $w=-1.125\pm0.092$ and $\sum m_ν<0.56$ eV. The redshift-dependent bias information thus provides a powerful, complementary cosmological probe, competitive with Ly-$\alpha$ analyses but subject to different systematics, and has the potential to approach sensitivity needed to distinguish neutrino mass hierarchies in future work.

Abstract

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 $\sum m_ν<0.28$eV at the 95% confidence level for a $ΛCDM + m_ν$ model, with a $σ_8$ equal to $σ_8=0.759\pm0.025$ (1$σ$). When we allow the dark energy equation of state parameter $w$ to vary we find $w=-1.30\pm0.19$ for a general $wCDM+m_ν$ model with the 95% confidence level upper limit on the neutrino masses at $\sum m_ν<0.59$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.

Figures (6)

• 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. Cooray:2005mmCooray:2006aq 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 Cooray:2005ksVale:2004ytMore:2008yy.
• 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 $\Lambda$CDM model. The x-axis magnitude values plotted are $M_r$ for SDSS, $M_B$ for DEEP2, and $M_{\rm UV}$ for LBGs at $z\sim 3.8$.
• Figure 3: constraints on the parameters of the $\Lambda$CDM+$m_{\nu}$ model from WMAP alone (blue), WMAP+LRG+bias data set at z=0.05 (green) and WMAP+LRG+all bias data sets (red).
• Figure 4: joint two-dimensional posterior probability contour plot in the $\sigma_8$-$n_s$ plane showing $68\%$ and $95\%$ contours from WMAP alone (red) and WMAP+LRG+bias data at all redshifts (green).
• Figure 5: joint two-dimensional posterior probability contour plot in the $\sigma_8$-$\sum m_{\nu}$ plane showing $68\%$ and $95\%$ contours from WMAP+LRG+bias data at all redshifts.