Cosmological Constraints from the SDSS Luminous Red Galaxies

TL;DR

This study measures the large-scale real-space galaxy power spectrum using SDSS LRGs and combines it with WMAP data to sharpen cosmological constraints. Employing a matrix-based PKL method, it delivers uncorrelated, minimum-variance P(k) estimates and robust tests against systematics, affirming the LCDM framework, detecting baryon oscillations, and constraining curvature, neutrino masses, and dark energy. The LRG data notably tighten parameter degeneracies, reducing uncertainties in Ωm, h, and Ωtot, while the analysis remains cautious about nonlinear modeling and FOG effects. The work demonstrates the complementary power of galaxy clustering and CMB data for precision cosmology and outlines pathways for even stronger tests with future surveys.

Abstract

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-Loeve 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/Mpc < k < 0.2h/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 LCDM 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 Om and the baryon fraction in good agreement with WMAP. Within the context of flat LCDM 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 two, giving Omega_m=0.24+-0.02 (1 sigma), sum m_nu < 0.9 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 LCDM framework, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint Omega_tot=1.05+-0.05 from WMAP alone to Omega_tot=1.003+-0.010. Assuming Omega_tot=1, the equation of state parameter is constrained to w=-0.94+-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/Mpc and associated nonlinear complications, yet agree well with more aggressive published analyses where nonlinear modeling is crucial.

Figures (25)

• Figure 1: The redshift distribution of the luminous red galaxies used is shown as a histogram and compared with the expected distribution in the absence of clustering, $\ln 10\times \int {\bar{n}}(r)r^3 d\Omega$ (solid curve) in comoving coordinates assuming a flat $\Omega_\Lambda=0.75$ cosmology. The bottom panel shows the ratio of observed and expected distributions. The four vertical lines delimit the NEAR, MID and FAR samples.
• Figure 2: The distribution of the 6,476 LRGs (black) and 32,417 main galaxies (green/grey) that are within $1.25^\circ$ of the Equatorial plane. The solid circles indicate the boundaries of our NEAR, MID and FAR subsamples. The "safe13" main galaxy sample analyzed here and in sdsspower is more local, extending out only to $600h^{-1}$ Mpc (dashed circle).
• Figure 3: The angular distribution of our LRGs is shown in Hammer-Aitoff projection in celestial coordinates, with the seven colors/greys indicating the seven angular subsamples that we analyze.
• Figure 4: Measured power spectra for the full LRG and main galaxy samples. Errors are uncorrelated and full window functions are shown in Figure \ref{['Wfig']}. The solid curves correspond to the linear theory $\Lambda$CDM fits to WMAP3 alone from Table 5 of Spergel06, normalized to galaxy bias $b=1.9$ (top) and $b=1.1$ (bottom) relative to the $z=0$ matter power. The dashed curves include the nonlinear correction of Cole05 for $A=1.4$, with $Q_{\rm nl}=30$ for the LRGs and $Q_{\rm nl}=4.6$ for the main galaxies; see equation (\ref{['QnlEq']}). The onset of nonlinear corrections is clearly visible for $k\mathrel{\hbox{$\mathchar"218$} \hbox{$\mathchar"13E$}} 0.09 h/$Mpc (vertical line).
• Figure 5: The window functions corresponding to the LRG band powers in Figure \ref{['all2powerFig']} are plotted, normalized to have unit peak height. Each window function typically peaks at the scale $k$ that the corresponding band power estimator was designed to probe.