PHYSICAL REVIEW D 74, 123507 (2006) Cosmological constraints from the SDSS luminous red galaxies Max Tegmark,1 Daniel J. Eisenstein,2 Michael A. Strauss,3 David H. Weinberg,4 Michael R. Blanton,5 Joshua A. Frieman,6,7 Masataka Fukugita,8 James E. Gunn,3 Andrew J. S. Hamilton,9 Gillian R. Knapp,3 Robert C. Nichol,10 Jeremiah P. Ostriker,3 Nikhil Padmanabhan,11 Will J. Percival,10 David J. Schlegel,12 Donald P. Schneider,13 Roman Scoccimarro,5 Urosˇ Seljak,11,14 Hee-Jong Seo,2 Molly Swanson,1 Alexander S. Szalay,15 Michael S. Vogeley,16 Jaiyul Yoo,4 Idit Zehavi,17 Kevork Abazajian,18 Scott F. Anderson,19 James Annis,7 Neta A. Bahcall,3 Bruce Bassett,20,21 Andreas Berlind,5 Jon Brinkmann,22 Tama´s Budavari,15 Francisco Castander,23 Andrew Connolly,24 Istvan Csabai,15 Mamoru Doi,25 Douglas P. Finkbeiner,3,26 Bruce Gillespie,22 Karl Glazebrook,15 Gregory S. Hennessy,27 David W. Hogg,5 Zˇ eljko Ivezic´,3,19 Bhuvnesh Jain,28 David Johnston,29,30 Stephen Kent,7 Donald Q. Lamb,6,31 Brian C. Lee,12,32 Huan Lin,7 Jon Loveday,33 Robert H. Lupton,3 Jeffrey A. Munn,27 Kaike Pan,22 Changbom Park,34 John Peoples,7 Jeffrey R. Pier,27 Adrian Pope,15 Michael Richmond,35 Constance Rockosi,6 Ryan Scranton,24 Ravi K. Sheth,28 Albert Stebbins,7 Christopher Stoughton,7 Istva´n Szapudi,36 Douglas L. Tucker,7 Daniel E. Vanden Berk,24 Brian Yanny,7 and Donald G. York6,31 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Department of Astronomy, University of Arizona, Tucson, Arizona 85721, USA 3Princeton University Observatory, Princeton, New Jersey 08544, USA 4Department of Astronomy, Ohio State University, Columbus, Ohio 43210, USA 5Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA 6Center for Cosmological Physics and Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA 7Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510, USA 8Institute for Cosmic Ray Research, University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa, Chiba, 277-8582, Japan 9JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, Colorado 80309, USA 10Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, P01 2EG, United Kingdom 11Department of Physics, Princeton University, Princeton, New Jersey 08544, USA 12Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 13Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, Pennsylvania 16802, USA 14International Center for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy 15Department of Physics and Astronomy, The Johns Hopkins University, 3701 San Martin Drive, Baltimore, Maryland 21218, USA 16Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA 17Department of Astronomy, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7215, USA 18Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 19Department of Astronomy, University of Washington, Box 351580, Seattle, Washington 98195, USA 20South African Astronomical Observatory, Cape Town, South Africa; 21Applied Mathematics Department, University of Cape Town, Cape Town, South Africa 22Apache Point Observatory, 2001 Apache Point Road, Sunspot, New Mexico 88349-0059, USA 23Institut d’Estudis Espacials de Catalunya/CSIC, Campus UAB, 08034 Barcelona, Spain 24University of Pittsburgh, Department of Physics and Astronomy, 3941 O’Hara Street, Pittsburgh, Pennsylvania 15260, USA 25Institute of Astronomy, University of Tokyo, Osawa 2-21-1, Mitaka, Tokyo, 181-0015, Japan 26Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS46, Cambridge, Massachusetts 02138, USA 27U.S. Naval Observatory, Flagstaff Station, 10391 W. Naval Observatory Road, Flagstaff, Arizona 86001-8521, USA 28Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 29Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena California, 91109, USA; 30California Institute of Technology, 1200 East California Boulevard, Pasadena, California 91125, USA 31Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA 32Gatan Inc., Pleasanton, California 94588, USA 33Sussex Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QJ, UK 34Department of Astronomy, Seoul National University, 151-742, Korea 35Physics Department, Rochester Institute of Technology, 1 Lomb Memorial Dr, Rochester, New York 14623, USA 36Institute for Astronomy, University of Hawaii, 2680, Woodlawn Drive, Honolulu, Hawaii 96822, USA (Received 22 August 2006; published 11 December 2006) 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-Loe`ve eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to 1550-7998=2006=74(12)=123507(34) 123507-1 © 2006 The American Physical Society MAX TEGMARK et al. PHYSICAL REVIEW D 74, 123507 (2006) 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 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 m and the baryon fraction in good agreement with WMAP. Within the context of flat CDM models, our LRG measurements complement WMAP by sharpening the constraints on the matter density,P the neutrino density and the tensor amplitude by about a factor of 2, giving m 0:24 0:02 (1), m & 0:9eV(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 CDM framework, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint tot 1:05 0:05 from WMAP alone to tot 1:003 0:010. Assuming tot 1, the equation of state parameter is constrained to w ÿ0:94 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. DOI: 10.1103/PhysRevD.74.123507 PACS numbers: 98.80.Es I. INTRODUCTION mation, and to explore the resulting constraints on cosmo- logical models. The emphasis of our cosmological analysis The dramatic recent progress by the Wilkinson will be on elucidating the links between cosmological Microwave Anisotropy Probe (WMAP) and other experi- parameters and observable features of the WMAP and ments [1–4] measuring the cosmic microwave background (CMB) has made non-CMB experiments even more im- SDSS power spectra, and on how these two data sets alone portant in the quest to constrain cosmological models and provide tight and robust constraints on many parameters their free parameters. These non-CMB constraints are that complement more aggressive but more systematics- crucially needed for breaking CMB degeneracies [5,6]; prone analyses of multiple data sets. for instance, WMAP alone is consistent with a closed In a parallel paper, Percival et al. [43] present a power universe with Hubble parameter h 0:3 and no cosmo- spectrum analysis of the Main Galaxy and LRG samples logical constant [7]. As long as the non-CMB constraints from the SDSS DR5 data set [44], which is a superset of the are less reliable and precise than the CMB, they will be the data used here. There are a number of differences in the limiting factor and weakest link in the precision cosmology analysis methods. Percival et al. use an FFT-based method endeavor. Much of the near-term progress in cosmology to estimate the angle-averaged (monopole) redshift-space will therefore be driven by reductions in statistical and galaxy power spectrum. We use a Pseudo-Karhunen-Loe`ve systematic uncertainties of non-CMB probes of the cosmic method [45,46] (see further discussion and references be- expansion history (e.g., SN Ia) and the matter power spec- low) to estimate the real-space (as opposed to redshift- trum (e.g., Lyman Forest, galaxy clustering and motions, space) galaxy power spectrum, using finger-of-god com- gravitational lensing, cluster studies and 21 cm pression and linear theory to remove redshift-space dis- tomography). tortion effects. In addition, the many technical decisions The cosmological constraining power of 3-dimensional that go into these analyses, regarding completeness correc- maps of the Universe provided by galaxy redshift surveys tions, angular masks, K-corrections and so forth, were has motivated ever more ambitious observational efforts made independently for the two papers, and they present such as the CfA/UZCPlease supply a definition for CfA/ different tests for systematic uncertainties. Despite these UZC. [8,9], LCRS [10], PSCz [11], DEEP [12], 2dFGRS many differences of detail, our conclusions agree to the [13], and SDSS [14] projects, resulting in progressively extent that they overlap (as discussed in Sec. III F and more accurate measurements of the galaxy power spectrum Appendix A 1), a reassuring indication of the robustness P k [15–30]. Constraints on cosmological models from of the results. these data sets have been most robust when the galaxy clustering could be measured on large scales where one has A.