Cosmological constraints from the SDSS luminous red galaxies

We measure the large-scale real-space power spectrum $P(k)$ using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimum-variance measurements in 20 $k$-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range $0.01h/\mathrm{Mpc}<k<0.2h/\mathrm{Mpc}$. Results from the LRG and main galaxy samples are consistent, with the former providing higher signal-to-noise. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. They provide a striking confirmation of the predicted large-scale $\Lambda \mathrm{CDM}$ power spectrum. Combining only SDSS LRG and WMAP data places robust constraints on many cosmological parameters that complement prior analyses of multiple data sets. The LRGs provide independent cross-checks on ${\Omega }_m$ and the baryon fraction in good agreement with WMAP. Within the context of flat $\Lambda \mathrm{CDM}$ models, our LRG measurements complement WMAP by sharpening the constraints on the matter density, the neutrino density and the tensor amplitude by about a factor of 2, giving ${\Omega }_m=0.24\pm 0.02$ ($1\sigma$), $\sum _{}^{}{m}_{\nu }\lesssim 0.9\mathrm{eV}$ (95%) and $r<0.3$ (95%). Baryon oscillations are clearly detected and provide a robust measurement of the comoving distance to the median survey redshift $z=0.35$ independent of curvature and dark energy properties. Within the $\Lambda \mathrm{CDM}$ framework, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint ${\Omega }_{\mathrm{tot}}=1.05\pm 0.05$ from WMAP alone to ${\Omega }_{\mathrm{tot}}=1.003\pm 0.010$. Assuming ${\Omega }_{\mathrm{tot}}=1$, the equation of state parameter is constrained to $w=-0.94\pm 0.09$, indicating the potential for more ambitious future LRG measurements to provide precision tests of the nature of dark energy. All these constraints are essentially independent of scales $k>0.1h/\mathrm{Mpc}$ and associated nonlinear complications, yet agree well with more aggressive published analyses where nonlinear modeling is crucial.