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We present a new method for calculating linear cosmic microwave background (CMB) anisotropy spectra based on integration over sources along the photon past light cone. In this approach the temperature anisotropy is written as a time integral over the product of a geometrical term and a source term. The geometrical term is given by radial eigenfunctions which do not depend on the particular cosmological model. The source term can be expressed in terms of photon, baryon and metric perturbations, all of which can be calculated using a small number of differential equations. This split clearly separates between the dynamical and geometrical effects on the CMB anisotropies. More importantly, it allows to significantly reduce the computational time compared to standard methods. This is achieved because the source term, which depends on the model and is generally the most time consuming part of calculation, is a slowly varying function of wavelength and needs to be evaluated only in a small number of points. The geometrical term, which oscillates much more rapidly than the source term, does not depend on the particular model and can be precomputed in advance. Standard methods that do not separate the two terms and require a much higher number of evaluations. The new method leads to about two orders of magnitude reduction in CPU time when compared to standard methods and typically requires a few minutes on a workstation for a single model. The method should be especially useful for accurate determinations of cosmological parameters from CMB anisotropy and polarization measurements that will become possible with the next generation of experiments. A programm implementing this method can be obtained from the authors.Subject headings: cosmology: cosmic microwave background, cosmology: large-scale structure of the universe, gravitation, cosmology: dark matter

We measure cosmological parameters using the three-dimensional power spectrum P (k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a "vanilla" flat adiabatic ΛCDM model without tilt (ns = 1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1σ constraints on the Hubble parameter from h ≈ 0.74−0.03 , on the matter density from Ωm ≈ 0.25 ± 0.10 to Ωm ≈ 0.30 ± 0.04 (1σ) and on neutrino masses from < 11 eV to < 0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0 ≈ 16.3 +2.3 −1.8 Gyr to t0 ≈ 14.1Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.

Using the formalism of spin-weighted functions we present an all-sky analysis of polarization in the Cosmic Microwave Background (CMB). Linear polarization is a second-rank symmetric and traceless tensor, which can be decomposed on a sphere into spin ±2 spherical harmonics. These are the analog of the spherical harmonics used in the temperature maps and obey the same completeness and orthogonality relations. We show that there exist two linear combinations of spin ±2 multipole moments which have opposite parities and can be used to fully characterize the statistical properties of polarization in the CMB. Magnetic-type parity combination does not receieve contributions from scalar modes and does not cross-correlate with either temperature or electric-type parity combination, so there are four different power spectra that fully characterize statistical properties of CMB. We present their explicit expressions for scalar and tensor modes in the form of line of sight integral solution and numerically evaluate them for a representative set of models. These general solutions differ from the expressions obtained previously in the small scale limit both for scalar and tensor modes. A method to generate and analyze all sky maps of temperature and polarization is given and the optimal estimators for various power spectra and their corresponding variances are discussed.98.70.V, 98.80.C

We investigate an analytic model to compute nonlinear power spectrum of dark matter, galaxies and their cross-correlation. The model is based on Press-Schechter halos, which cluster and have realistic dark matter profiles. The total power spectrum is a sum of two contributions, one from correlations betwen the halos and one from correlations within the same halo. We show that such a model can give dark matter power spectra which match well with the results of N-body simulations, provided that concentration parameter decreases with the halo mass. Galaxy power spectrum differs from dark matter power spectrum because pair weighted number of galaxies increases less rapidly than the halo mass, as predicted by theoretical models and observed in clusters. In this case the resulting power spectrum becomes a power law with the slope closed to the observed. Such a model also predicts a later onset of nonlinear clustering compared to the dark matter, which is needed to reconcile the CDM models with the data. Generic prediction of this model is that bias is scale dependent and nonmonotonic. For red or elliptical galaxies bias in power spectrum may be scale dependent even on very large scales. Our predictions for galaxy-dark matter correlations, which can be observed through the galaxy-galaxy lensing, show that these cannot be interpreted simply as an average halo profile of a typical galaxy, because different halo masses dominate at different scales and because larger halos host more than one galaxy. We discuss the prospects of using cross-correlations in combination with galaxy clustering to determine the dark matter power spectrum (ABRIDGED).Comment: 16 pages, 7 figures, submitted to Phys. Rev.

We measure the large-scale real-space power spectrum P (k) using a sample of 205,443 galaxies from the Sloan Digital Sky Survey, covering 2417 effective square degrees with mean redshift z ≈ 0.1. We employ a matrix-based method using pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimumvariance measurements in 22 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 0.02 h/Mpc < k < 0.3 h/Mpc. We pay particular attention to modeling, quantifying and correcting for potential systematic errors, nonlinear redshift distortions and the artificial red-tilt caused by luminosity-dependent bias. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. Our final result is a measurement of the real-space matter power spectrum P (k) up to an unknown overall multiplicative bias factor. Our calculations suggest that this bias factor is independent of scale to better than a few percent for k < 0.1 h/Mpc, thereby making our results useful for precision measurements of cosmological parameters in conjunction with data from other experiments such as the WMAP satellite. The power spectrum is not well-characterized by a single power law, but unambiguously shows curvature. As a simple characterization of the data, our measurements are well fit by a flat scaleinvariant adiabatic cosmological model with hΩ m = 0.213 ± 0.023 and σ 8 = 0.89 ± 0.02 for L * galaxies, when fixing the baryon fraction Ω b /Ω m = 0.17 and the Hubble parameter h = 0.72; cosmological interpretation is given in a companion paper.

The relationship between galaxies and dark matter (DM) can be characterized by the halo mass of the central galaxy and the fraction of galaxies that are satellites. Here, we present observational constraints from the Sloan Digital Sky Survey on these quantities as a function of r-band luminosity and stellar mass using galaxy-galaxy weak lensing, with a total of 351 507 lenses. We use stellar masses derived from spectroscopy and virial halo masses derived from weak gravitational lensing to determine the efficiency with which baryons in the halo of the central galaxy have been converted into stars. We find that an L * galaxy with a stellar mass of 6 × 10 10 M is hosted by a halo with mass of 1.4 × 10 12 h −1 M , independent of morphology, yielding baryon conversion efficiencies of 17 +10 −5 per cent (early-types) and 16 +15 −6 per cent (latetypes) at the 95 per cent confidence level (statistical, not including systematic uncertainty due to assumption of a universal initial mass function). We find that for a given stellar mass, the halo mass is independent of morphology below M stellar = 10 11 M , in contrast to typically a factor of 2 difference in halo mass between ellipticals and spirals at a fixed luminosity. This suggests that stellar mass is a good proxy for halo mass in this range and should be used preferentially whenever a halo mass selected sample is needed. For higher stellar masses, the conversion efficiency is a declining function of stellar mass, and the differences in halo mass between early-and late-types become larger, reflecting the fact that most group and cluster haloes with masses above 10 13 M host ellipticals at the centre, while even the brightest central spirals are hosted by haloes of mass below 10 13 M . We find that the fraction of spirals that are satellites is roughly 10-15 per cent independent of stellar mass or luminosity, while for ellipticals this fraction decreases with stellar mass from 50 per cent at 10 10 M to 10 per cent at 3 × 10 11 M or 20 per cent at the maximum luminosity considered. We split the elliptical sample by local density, and find that at a given luminosity there is no difference in the signal on scales below 100 h −1 kpc between high-and low-density regions, suggesting that tidal stripping inside large haloes does not remove most of the DM from the early-type satellites. This result is dominated by haloes in the mass range 10 13 -10 14 h −1 M , and is an average over all separations from the group or cluster centre.

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 0.01 h/Mpc < k < 0.2 h/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 ΛCDM 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 Ωm and the baryon fraction in good agreement with WMAP. Within the context of flat ΛCDM 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 Ωm = 0.24±0.02 (1σ), mν ∼ < 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 ΛCDM framework, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint Ωtot = 1.05±0.05 from WMAP alone to Ωtot = 1.003 ± 0.010. Assuming Ωtot = 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. k [h/Mpc] Power Pg 0.012 +0.005 −0.004 124884 ± 18775 0.015 +0.003 −0.002 118814 ± 29400 0.018 +0.004 −0.002 134291 ± 21638 0.021 +0.004 −0.003 58644 ± 16647 0.024 +0.004 −0.003 105253 ± 12736 0.028 +0.005 −0.003 77699 ± 9666 0.032 +0.005 −0.003 57870 ± 7264 0.037 +0.006 −0.004 56516 ± 5466 0.043 +0.008 −0.006 50125 ± 3991 0.049 +0.008 −0.007 45076 ± 2956 0.057 +0.009 −0.007 39339 ± 2214 0.065 +0.010 −0.008 39609 ± 1679 0.075 +0.011 −0.009 31566 ± 1284 0.087 +0.