Theoretical uncertainty in baryon oscillations

We discuss the systematic uncertainties in the recovery of dark energy properties from the use of baryon acoustic oscillations as a standard ruler. We demonstrate that while unknown relativistic components in the universe prior to recombination would alter the sound speed, the inferences for dark energy from low-redshift surveys are unchanged so long as the microwave background anisotropies can measure the redshift of matter-radiation equality, which they can do to sufficient accuracy. The mismeasurement of the radiation and matter densities themselves (as opposed to their ratio) would manifest as an incorrect prediction for the Hubble constant at low redshift. In addition, these anomalies do produce subtle but detectable features in the microwave anisotropies.Comment: 4 pages, REVTeX, 1 figure. Submitted to PR

RascalC: A Jackknife Approach to Estimating Single and Multi-Tracer Galaxy Covariance Matrices

To make use of clustering statistics from large cosmological surveys, accurate and precise covariance matrices are needed. We present a new code to estimate large scale galaxy two-point correlation function (2PCF) covariances in arbitrary survey geometries that, due to new sampling techniques, runs $\sim 10^4$ times faster than previous codes, computing finely-binned covariance matrices with negligible noise in less than 100 CPU-hours. As in previous works, non-Gaussianity is approximated via a small rescaling of shot-noise in the theoretical model, calibrated by comparing jackknife survey covariances to an associated jackknife model. The flexible code, RascalC, has been publicly released, and automatically takes care of all necessary pre- and post-processing, requiring only a single input dataset (without a prior 2PCF model). Deviations between large scale model covariances from a mock survey and those from a large suite of mocks are found to be be indistinguishable from noise. In addition, the choice of input mock are shown to be irrelevant for desired noise levels below $\sim 10^5$ mocks. Coupled with its generalization to multi-tracer data-sets, this shows the algorithm to be an excellent tool for analysis, reducing the need for large numbers of mock simulations to be computed.Comment: 29 pages, 8 figures. Accepted by MNRAS. Code is available at http://github.com/oliverphilcox/RascalC with documentation at http://rascalc.readthedocs.io

Cosmic homogeneity demonstrated with luminous red galaxies

We test the homogeneity of the Universe at $z\sim 0.3$ with the Luminous Red Galaxy (LRG) spectroscopic sample of the Sloan Digital Sky Survey. First, the mean number $N(R)$ of LRGs within completely surveyed LRG-centered spheres of comoving radius $R$ is shown to be proportional to $R^3$ at radii greater than $R\sim 70 h^{-1} \mathrm{Mpc}$. The test has the virtue that it does not rely on the assumption that the LRG sample has a finite mean density; its results show, however, that there \emph{is} such a mean density. Secondly, the survey sky area is divided into 10 disjoint solid angular regions and the fractional rms density variations of the LRG sample in the redshift range $0.2<z<0.35$ among these ($\sim 2\times10^7 h^{-3} \mathrm{Mpc^3}$) regions is found to be 7 percent of the mean density. This variance is consistent with typical biased \lcdm models and puts very strong constraints on the quality of SDSS photometric calibration.Comment: submitted to Ap

Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys

We show that the measurement of the baryonic acoustic oscillations in large high redshift galaxy surveys offers a precision route to the measurement of dark energy. The cosmic microwave background provides the scale of the oscillations as a standard ruler that can be measured in the clustering of galaxies, thereby yielding the Hubble parameter and angular diameter distance as a function of redshift. This, in turn, enables one to probe dark energy. We use a Fisher matrix formalism to study the statistical errors for redshift surveys up to z=3 and report errors on cosmography while marginalizing over a large number of cosmological parameters including a time-dependent equation of state. With redshifts surveys combined with cosmic microwave background satellite data, we achieve errors of 0.037 on Omega_x, 0.10 on w(z=0.8), and 0.28 on dw(z)/dz for cosmological constant model. Models with less negative w(z) permit tighter constraints. We test and discuss the dependence of performance on redshift, survey conditions, and fiducial model. We find results that are competitive with the performance of future supernovae Ia surveys. We conclude that redshift surveys offer a promising independent route to the measurement of dark energy.Comment: submitted to ApJ, 24 pages, LaTe

Small Scale Perturbations in a General MDM Cosmology

For a universe with massive neutrinos, cold dark matter, and baryons, we solve the linear perturbation equations analytically in the small-scale limit and find agreement with numerical codes at the 1-2% level. The inclusion of baryons, a cosmological constant, or spatial curvature reduces the small-scale power and tightens limits on the neutrino density from observations of high redshift objects. Using the asymptotic solution, we investigate neutrino infall into potential wells and show that it can be described on all scales by a growth function that depends on time, wavenumber, and cosmological parameters. The growth function may be used to scale the present-day transfer functions back in redshift. This allows us to construct the time-dependent transfer function for each species from a single master function that is independent of time, cosmological constant, and curvature.Comment: Submitted to ApJ; 13 pages, aastex, 4 figures included; also available at http://www.sns.ias.edu/~wh

The Clustering of Luminous Red Galaxies in the Sloan Digital Sky Survey Imaging Data

We present the 3D real space clustering power spectrum of a sample of \~600,000 luminous red galaxies (LRGs) measured by the Sloan Digital Sky Survey (SDSS), using photometric redshifts. This sample of galaxies ranges from redshift z=0.2 to 0.6 over 3,528 deg^2 of the sky, probing a volume of 1.5 (Gpc/h)^3, making it the largest volume ever used for galaxy clustering measurements. We measure the angular clustering power spectrum in eight redshift slices and combine these into a high precision 3D real space power spectrum from k=0.005 (h/Mpc) to k=1 (h/Mpc). We detect power on gigaparsec scales, beyond the turnover in the matter power spectrum, on scales significantly larger than those accessible to current spectroscopic redshift surveys. We also find evidence for baryonic oscillations, both in the power spectrum, as well as in fits to the baryon density, at a 2.5 sigma confidence level. The statistical power of these data to constrain cosmology is ~1.7 times better than previous clustering analyses. Varying the matter density and baryon fraction, we find \Omega_M = 0.30 \pm 0.03, and \Omega_b/\Omega_M = 0.18 \pm 0.04, The detection of baryonic oscillations also allows us to measure the comoving distance to z=0.5; we find a best fit distance of 1.73 \pm 0.12 Gpc, corresponding to a 6.5% error on the distance. These results demonstrate the ability to make precise clustering measurements with photometric surveys (abridged).Comment: 23 pages, 27 figures, submitted to MNRA