We compute the angular power spectrum C_l from 1.5 milliongalaxies in early Sloan Digital Sky Survey (SDSS) data on large angularscales, l<~600. The data set covers about 160 deg², with acharacteristic depth on the order of 1 h^-1 Gpc in thefaintest (21*<22) of our four magnitude bins.Cosmological interpretations of these results are presented in acompanion paper by Dodelson and coworkers. The data in all fourmagnitude bins are consistent with a simple flat ``concordance'' modelwith nonlinear evolution and linear bias factors on the order of unity.Nonlinear evolution is particularly evident for the brightest galaxies.A series of tests suggests that systematic errors related to seeing,reddening, etc. are negligible, which bodes well for the 60-fold largersample that the SDSS is currently collecting. Uncorrelated error barsand well-behaved window functions make our measurements a convenientstarting point for cosmological model fitting.

Early photometric data from the Sloan Digital Sky Survey (SDSS) containangular positions for 1.5 million galaxies. In companion papers, theangular correlation function w(θ) and two-dimensional powerspectrum C_l of these galaxies are presented. Here we invertLimber's equation to extract the three-dimensional power spectrum fromthe angular results. We accomplish this using an estimate of dn/dz, theredshift distribution of galaxies in four different magnitude slices inthe SDSS photometric catalog. The resulting three-dimensional powerspectrum estimates from w(θ) and C_l agree with eachother and with previous estimates over a range in wavenumbers0.03-1)<1. The galaxies in the faintestmagnitude bin (21*<22, which have median redshiftz_m=0.43) are less clustered than the galaxies in thebrightest magnitude bin (18*<19 withz_m=0.17), especially on scales where nonlinearities areimportant. The derived power spectrum agrees with that of Szalay et al.,who go directly from the raw data to a parametric estimate of the powerspectrum. The strongest constraints on the shape parameter Γ comefrom the faintest galaxies (in the magnitude bin21*<22), from which we infer

We describe the algorithm that selects the main sample of galaxies forspectroscopy in the Sloan Digital Sky Survey (SDSS) from the photometricdata obtained by the imaging survey. Galaxy photometric properties aremeasured using the Petrosian magnitude system, which measures flux inapertures determined by the shape of the surface brightness profile. Themetric aperture used is essentially independent of cosmological surfacebrightness dimming, foreground extinction, sky brightness, and thegalaxy central surface brightness. The main galaxy sample consists ofgalaxies with r-band Petrosian magnitudes r<=17.77 and r-bandPetrosian half-light surface brightnesses μ₅₀<=24.5 magarcsec^-2. These cuts select about 90 galaxy targets persquare degree, with a median redshift of 0.104. We carry out a number oftests to show that (1) our star-galaxy separation criterion is effectiveat eliminating nearly all stellar contamination while removing almost nogenuine galaxies, (2) the fraction of galaxies eliminated by our surface

We discuss the optical and radio properties of ~30,000 FIRST (radio, 20cm, sensitive to 1 mJy) sources positionally associated within 1.5" witha Sloan Digital Sky Survey (SDSS) (optical, sensitive to r*~22.2) source

The Sloan Digital Sky Survey is one of the first multicolor photometricand spectroscopic surveys designed to measure the statistical propertiesof galaxies within the local universe. In this paper we present some ofthe initial results on the angular two-point correlation functionmeasured from the early SDSS galaxy data. The form of the correlationfunction, over the magnitude interval 18*<22, isshown to be consistent with results from existing wide-field,photographic-based surveys and narrower CCD galaxy surveys. On scalesbetween 1' and 1° the correlation function is well described by apower law with an exponent of ~-0.7. The amplitude of the correlationfunction, within this angular interval, decreases with faintermagnitudes in good agreement with analysis from existing galaxy surveys.There is a characteristic break in the correlation function on scales ofapproximately 1°-2°. On small scales, θ<1^',the SDSS correlation function does not appear to be consistent with thepower-law form fitted to the 1^'<θ<0.5d data.

The angular distribution of galaxies encodes a wealth of informationabout large-scale structure. Ultimately, the Sloan Digital Sky Survey(SDSS) will record the angular positions of order of 10⁸galaxies in five bands, adding significantly to the cosmologicalconstraints. This is the first in a series of papers analyzing arectangular stripe of 2.5d×90^deg from early SDSS data.We present the angular correlation function for galaxies in fourseparate magnitude bins on angular scales ranging from 0.003d to15°. Much of the focus of this paper is on potential systematiceffects. We show that the final galaxy catalog-with the mask accountingfor regions of poor seeing, reddening, bright stars, etc.-is free fromexternal and internal systematic effects for galaxies brighter thanr^*=22. Our estimator of the angular correlation functionincludes the effects of the integral constraint and the mask. The fullcovariance matrix of errors in these estimates is derived using mockcatalogs with further estimates using a number of other methods. Basedon observations obtained with the Sloan Digital Sky Survey.

We reconsider the inference of spatial power spectra from angularclustering data and show how to include correlations in both the angularcorrelation function and the spatial power spectrum. Inclusion of thefull covariance matrices loosens the constraints on large-scalestructure inferred from the Automated Plate Measuring (APM) survey byover a factor of 2. We present a new inversion technique based onsingular-value decomposition that allows one to propagate the covariancematrix on the angular correlation function through to that of thespatial power spectrum and to reconstruct smooth power spectra withoutunderestimating the errors. Within a parameter space of the cold darkmatter (CDM) shape Γ and the amplitude σ₈, wefind that the angular correlations in the APM survey constrain Γ

The large-scale structure of high-redshift galaxies produces correlatedanisotropy in the far-infrared background (FIRB). In regions of the skywhere the thermal emission from Galactic dust is well below average,these high-redshift correlations may be the most significant source ofangular fluctuation power over a wide range of angular scales, from ~7'to ~3°, and frequencies, from ~400 to ~1000 GHz. The strength ofthis signal should allow detailed studies of the statistics of the FIRBfluctuations, including the shape of the angular power spectrum at agiven frequency and the degree of coherence between FIRB maps atdifferent frequencies. The FIRB correlations depend on and henceconstrain the redshift-dependent spectral energy distributions, numbercounts, and clustering bias of the galaxies and active nuclei thatcontribute to the background. We quantify the accuracy to which Planckand a newly proposed balloon-borne mission, Explorer of Diffuse GalacticEmissions, could constrain models of the high-redshift universe throughthe measurement of FIRB fluctuations. We conclude that the average bias

In the course of its commissioning observations, the Sloan Digital SkySurvey (SDSS) has produced one of the largest redshift samples ofgalaxies selected from CCD images. Using 11,275 galaxies complete tor^*=17.6 over 140 deg², we compute the luminosityfunction of galaxies in the r^* band over a range-23r^*<-16 (for h=1). The result iswell-described by a Schechter function with parametersφ_*=(1.46+/-0.12)×10^-2 h³Mpc^-3, M_*=-20.83+/-0.03, and α=-1.20+/-0.03.The implied luminosity density in r^* isj~(2.6+/-0.3)×10⁸h L_solar Mpc^-3.We find that the surface brightness selection threshold has a negligibleimpact for M_r^*<-18. Using subsets of the data,we measure the luminosity function in the u^*, g^*,i^*, and z^* bands as well; the slope at lowluminosities ranges from α=-1.35 to α=-1.2. We measure thebivariate distribution of r^* luminosity with half-lightsurface brightness, intrinsic g^*-r^* color, andmorphology. In agreement with previous studies, we find that highsurface brightness, red, highly concentrated galaxies are on averagemore luminous than low surface brightness, blue, less concentratedgalaxies. An important feature of the SDSS luminosity function is theuse of Petrosian magnitudes, which measure a constant fraction of agalaxy's total light regardless of the amplitude of its surfacebrightness profile. If we synthesize results for R_GKC band orb_j band using these Petrosian magnitudes, we obtainluminosity densities 2 times that found by the Las Campanas RedshiftSurvey in R_GKC and 1.4 times that found by the Two DegreeField Galaxy Redshift Survey in b_j. However, we are able toreproduce the luminosity functions obtained by these surveys if we alsomimic their isophotal limits for defining galaxy magnitudes, which areshallower and more redshift dependent than the Petrosian magnitudes usedby the SDSS. Based on observations obtained with the Sloan Digital SkySurvey.

We describe the target selection and resulting properties of aspectroscopic sample of luminous red galaxies (LRGs) from the imagingdata of the Sloan Digital Sky Survey (SDSS). These galaxies are selectedon the basis of color and magnitude to yield a sample of luminousintrinsically red galaxies that extends fainter and farther than themain flux-limited portion of the SDSS galaxy spectroscopic sample. Thesample is designed to impose a passively evolving luminosity andrest-frame color cut to a redshift of 0.38. Additional, yet moreluminous red galaxies are included to a redshift of ~0.5. Approximately12 of these galaxies per square degree are targeted for spectroscopy, sothe sample will number over 100,000 with the full survey. SDSScommissioning data indicate that the algorithm efficiently selectsluminous (M^*_g~-21.4) red galaxies, that thespectroscopic success rate is very high, and that the resulting set ofgalaxies is approximately volume limited out to z=0.38. When the SDSS iscomplete, the LRG spectroscopic sample will fill over 1 h^-3Gpc³ with an approximately homogeneous population of galaxiesand will therefore be well suited to studies of large-scale structureand clusters out to z=0.5.

One of the main challenges facing upcoming cosmic microwave background(CMB) experiments will be to distinguish the cosmological signal fromforeground contamination. We present a comprehensive treatment of thisproblem and study how foregrounds degrade the accuracy with which theBoomerang, MAP, and Planck experiments can measure cosmologicalparameters. Our foreground model includes not only the normalization,frequency dependence, and scale dependence for each physical component,but also variations in frequency dependence across the sky. Whenestimating how accurately cosmological parameters can be measured, weinclude the important complication that foreground model parameters (weuse about 500) must be simultaneously measured from the data as well.Our results are quite encouraging: despite all these complications,precision measurements of most cosmological parameters are degraded byless than a factor of 2 for our main foreground model and by less than afactor of 5 in our most pessimistic scenario. Parameters measured thoughlarge-angle polarization signals suffer more degradation: up to 5 in themain model and 25 in the pessimistic case. The foregrounds that arepotentially most damaging and therefore most in need of further studyare vibrating dust emission and point sources, especially those in theradio frequencies. It is well known that E and B polarization containvaluable information about reionization and gravity waves, respectively.However, the cross-correlation between polarized and unpolarizedforegrounds also deserves further study, as we find that it carries thebulk of the polarization information about most other cosmologicalparameters.

The Sloan Digital Sky Survey (SDSS) will provide the data to supportdetailed investigations of the distribution of luminous and nonluminousmatter in the universe: a photometrically and astrometrically calibrateddigital imaging survey of π sr above about Galactic latitude 30°in five broad optical bands to a depth of g'~23 mag, and a spectroscopicsurvey of the approximately 10⁶ brightest galaxies and10⁵ brightest quasars found in the photometric object catalogproduced by the imaging survey. This paper summarizes the observationalparameters and data products of the SDSS and serves as an introductionto extensive technical on-line documentation.

The bulk of recent cosmological research has focused on the adiabaticcold dark matter model and its simple extensions. Here we present anaccurate fitting formula that describes the matter transfer functions ofall common variants, including mixed dark matter models. The result is afunction of wavenumber, time, and six cosmological parameters: themassive neutrino density, number of neutrino species degenerate in mass,baryon density, Hubble constant, cosmological constant, and spatialcurvature. We show how observational constraints-e.g., the shape of thepower spectrum, the abundance of clusters and damped Lyalpha systems,and the properties of the Lyalpha forest-can be extended to a wide rangeof cosmologies, which includes variations in the neutrino and baryonfractions in both high-density and low-density universes.

We study the ability of future cosmic microwave background anisotropyexperiments and redshift surveys to constrain a 13-dimensionalparameterization of the adiabatic cold dark matter model. Each alone isunable to determine all parameters to high accuracy. However, consideredtogether, one data set resolves the difficulties of the other, allowingcertain degenerate parameters to be determined with far greaterprecision. We treat in detail the degeneracies involving the classicalcosmological parameters, massive neutrinos, tensor-scalar ratio, bias,and reionization optical depth as well as how redshift surveys canresolve them. We discuss the opportunities for internal and externalconsistency checks on these measurements. Previous papers on parameterestimation have generally treated smaller parameter spaces; in directcomparisons to these works, we tend to find weaker constraints andsuggest numerical explanations for the discrepancies.

We study the general structure of models for structure formation, withapplications to the reverse engineering of the model from observations.Through a careful accounting of the degrees of freedom in covariantgravitational instability theory, we show that the evolution ofstructure is completely specified by the stress history of the darksector. The study of smooth, entropic, sonic, scalar anisotropic, vectoranisotropic, and tensor anisotropic stresses reveals the origin,robustness, and uniqueness of specific model phenomenology. We constructuseful and illustrative analytic solutions that cover cases withmultiple species of differing equations of state relevant to the currentgeneration of models, especially those with effectively smoothcomponents. We present a simple case study of models withphenomenologies similar to that of a ΛCDM model to highlightreverse-engineering issues. A critical-density universe dominated by asingle type of dark matter with the appropriate stress history can mimica ΛCDM model exactly.

Determining the properties of the dark components of the universeremains one of the outstanding challenges in cosmology. We explore howupcoming CMB anisotropy measurements, galaxy power spectrum data, andsupernova (SN) distance measurements can observationally constrain theirgravitational properties with minimal assumptions on the theoreticalside. SN observations currently suggest the existence of dark matterwith an exotic equation of state p/ρ<~-1/3 that accelerates theexpansion of the universe. When combined with CMB anisotropymeasurements, SN or galaxy survey data can in principle determine theequation of state and density of this component separately, regardlessof their value, as long as the universe is spatially flat. Combiningthese pairs creates a sharp consistency check. If p/ρ>~-1/2, thenthe clustering behavior (sound speed) of the dark component can bedetermined so as to test the scalar-field ``quintessence'' hypothesis.If the exotic matter turns out instead to be simply a cosmologicalconstant (p/ρ=-1), the combination of CMB and galaxy survey datashould provide a significant detection of the remaining dark matter, theneutrino background radiation (NBR). The gross effect of its density ortemperature on the expansion rate is ill constrained as it can bemimicked by a change in the matter density. However, anisotropies of theNBR break this degeneracy and should be detectable by upcomingexperiments.

We assess the possibility that baryonic acoustic oscillations inadiabatic models may explain the observations of excess power inlarge-scale structure on 100 h-1 Mpc scales. The observed locationrestricts models to two extreme areas of parameter space. In eithercase, the baryon fraction must be large ( Omega _b/ Omega₀>~0.3 ) in order to yield significant features. The firstregion requires Omega ₀<~0.2 h to match the location,implying large blue tilts ( n>~1.4 ) to satisfy cluster abundanceconstraints. The power spectrum also continues to rise toward largerscales in these models. The second region requires Omega ₀~1, implying Omega _b well out of the range of big bangnucleosynthesis constraints; moreover, the peak is noticeably wider thanthe observations suggest. Testable features of both solutions are thatthey require moderate reionization and thereby generate potentiallyobservable (~1 mu K) large-angle polarization, as well as subarcminutetemperature fluctuations. In short, baryonic features in adiabaticmodels may explain the observed excess only if currently favoreddeterminations of cosmological parameters are in substantial error or ifpresent surveys do not represent a fair sample of 100 h-1 Mpcstructures.

We provide scaling relations and fitting formulae for adiabatic colddark matter cosmologies that account for all baryon effects in the

We describe a new method (HOP) for identifying groups of particles inN-body simulations. Having assigned to every particle an estimate of itslocal density, we associate each particle with the densest of the Nhopparticles nearest to it. Repeating this process allows us to trace apath, within the particle set itself, from each particle in thedirection of increasing density. The path ends when it reaches aparticle that is its own densest neighbor; all particles reaching thesame such particle are identified as a group. Combined with an adaptivesmoothing kernel for finding the densities, this method is spatiallyadaptive, coordinate-free, and numerically straightforward. One canproceed to process the output by truncating groups at a particulardensity contour and combining groups that share a (possibly different)density contour. While the resulting algorithm has several user-chosenparameters, we show that the results are insensitive to most of these,the exception being the outer density cutoff of the groups.

For a universe with massive neutrinos, cold dark matter, and baryons, wesolve the linear perturbation equations analytically in the small-scale