Anisotropic measurements of the Baryon Acoustic Oscillation (BAO) feature within a galaxy survey enable joint inference about the Hubble parameter $H(z)$ and angular diameter distance $D_A(z)$. These measurements are typically obtained from moments o
f the measured 2-point clustering statistics, with respect to the cosine of the angle to the line of sight $mu$. The position of the BAO features in each moment depends on a combination of $D_A(z)$ and $H(z)$, and measuring the positions in two or more moments breaks this parameter degeneracy. We derive analytic formulae for the parameter combinations measured from moments given by Legendre polynomials, power laws and top-hat Wedges in $mu$, showing explicitly what is being measured by each in real-space for both the correlation function and power spectrum, and in redshift-space for the power spectrum. The large volume covered by modern galaxy samples means that the correlation function can be well approximated as having no correlations at different $mu$ on the BAO scale, and that the errors on this scale are approximately independent of $mu$. Using these approximations, we derive the information content of various moments. We show that measurements made using either the monopole and quadrupole, or the monopole and $mu^2$ power-law moment, are optimal for anisotropic BAO measurements, in that they contain all of the available information using two moments, the minimal number required to measure both $H(z)$ and $D_A(z)$. We test our predictions using 600 mock galaxy samples, matched to the SDSS-III Baryon Oscillation Spectroscopic Survey CMASS sample, finding a good match to our analytic predictions. Our results should enable the optimal extraction of information from future galaxy surveys such as eBOSS, DESI and Euclid.
We apply a new method to measure primordial non-Gaussianity, using the cross-correlation between galaxy surveys and the CMB lensing signal to measure galaxy bias on very large scales, where local-type primordial non-Gaussianity predicts a $k^2$ diver
gence. We use the CMB lensing map recently published by the Planck collaboration, and measure its external correlations with a suite of six galaxy catalogues spanning a broad redshift range. We then consistently combine correlation functions to extend the recent analysis by Giannantonio et al. (2013), where the density-density and the density-CMB temperature correlations were used. Due to the intrinsic noise of the Planck lensing map, which affects the largest scales most severely, we find that the constraints on the galaxy bias are similar to the constraints from density-CMB temperature correlations. Including lensing constraints only improves the previous statistical measurement errors marginally, and we obtain $ f_{mathrm{NL}} = 12 pm 21 $ (1$sigma$) from the combined data set. However, the lensing measurements serve as an excellent test of systematic errors: we now have three methods to measure the large-scale, scale-dependent bias from a galaxy survey: auto-correlation, and cross-correlation with both CMB temperature and lensing. As the publicly available Planck lensing maps have had their largest-scale modes at multipoles $l<10$ removed, which are the most sensitive to the scale-dependent bias, we consider mock CMB lensing data covering all multipoles. We find that, while the effect of $f_{mathrm{NL}}$ indeed increases significantly on the largest scales, so do the contributions of both cosmic variance and the intrinsic lensing noise, so that the improvement is small.
We present the strongest robust constraints on primordial non-Gaussianity (PNG) from currently available galaxy surveys, combining large-scale clustering measurements and their cross-correlations with the cosmic microwave background. We update the da
ta sets used by Giannantonio et al. (2012), and broaden that analysis to include the full set of two-point correlation functions between all surveys. In order to obtain the most reliable constraints on PNG, we advocate the use of the cross-correlations between the catalogs as a robust estimator and we perform an extended analysis of the possible systematics to reduce their impact on the results. To minimize the impact of stellar contamination in our luminous red galaxy (LRG) sample, we use the recent Baryon Oscillations Spectroscopic Survey catalog of Ross et al. (2011). We also find evidence for a new systematic in the NVSS radio galaxy survey similar to, but smaller than, the known declination-dependent issue; this is difficult to remove without affecting the inferred PNG signal, and thus we do not include the NVSS auto-correlation function in our analyses. We find no evidence of primordial non-Gaussianity; for the local-type configuration we obtain for the skewness parameter $ -36 < f_{mathrm{NL}} < 45 $ at 95 % c.l. ($5 pm 21$ at $1sigma$) when using the most conservative part of our data set, improving previous results; we also find no evidence for significant kurtosis, parameterized by $g_{mathrm{NL}}$. In addition to PNG, we simultaneously constrain dark energy and find that it is required with a form consistent with a cosmological constant.
We measure the sum of the neutrino particle masses using the three-dimensional galaxy power spectrum of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) CMASS galaxy sample. Combined with the cosmic microwave backgroun
d (CMB), supernova (SN) and additional baryonic acoustic oscillation (BAO) data, we find upper 95 percent confidence limits of the neutrino mass $Sigma m_{ u}<0.340$ eV within a flat $Lambda$CDM background, and $Sigma m_{ u}<0.821$ eV, assuming a more general background cosmological model. The number of neutrino species is measured to be $N_{rm eff}=4.308pm0.794$ and $N_{rm eff}=4.032^{+0.870}_{-0.894}$ for these two cases respectively. We study and quantify the effect of several factors on the neutrino measurements, including the galaxy power spectrum bias model, the effect of redshift-space distortion, the cutoff scale of the power spectrum, and the choice of additional data. The impact of neutrinos with unknown masses on other cosmological parameter measurements is investigated. The fractional matter density and the Hubble parameter are measured to be $Omega_M=0.2796pm0.0097$, $H_0=69.72^{+0.90}_{-0.91}$ km/s/Mpc (flat $Lambda$CDM) and $Omega_M=0.2798^{+0.0132}_{-0.0136}$, $H_0=73.78^{+3.16}_{-3.17}$ km/s/Mpc (more general background model). Based on a Chevallier-Polarski-Linder (CPL) parametrisation of the equation-of-state $w$ of dark energy, we find that $w=-1$ is consistent with observations, even allowing for neutrinos. Similarly, the curvature Omega_K and the running of the spectral index $alpha_s$ are both consistent with zero. The tensor-to-scaler ratio is constrained down to $r<0.198$ (95 percent CL, flat $Lambda$ CDM) and $r<0.440$ (95 percent CL, more general background model).
We analyze the density field of 264,283 galaxies observed by the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) and included in the SDSS data release nine (DR9). In total, the SDSS DR9 BOSS data includes spectrosco
pic redshifts for over 400,000 galaxies spread over a footprint of more than 3,000 deg^2. We measure the power spectrum of these galaxies with redshifts 0.43 < z < 0.7 in order to constrain the amount of local non-Gaussianity, f_NL,local, in the primordial density field, paying particular attention to the impact of systematic uncertainties. The BOSS galaxy density field is systematically affected by the local stellar density and this influences the ability to accurately measure f_NL,local. In the absence of any correction, we find (erroneously) that the probability that f_NL,local is greater than zero, P(f_NL,local >0), is 99.5%. After quantifying and correcting for the systematic bias and including the added uncertainty, we find -45 < f_NL,local < 195 at 95% confidence, and P(f_NL,local >0) = 91.0%. A more conservative approach assumes that we have only learned the k-dependence of the systematic bias and allows any amplitude for the systematic correction; we find that the systematic effect is not fully degenerate with that of f_NL,local, and we determine that -82 < f_NL,local < 178 (at 95% confidence) and P(f_NL,local >0) = 68%. This analysis demonstrates the importance of accounting for the impact of Galactic foregrounds on f_NL,local measurements. We outline the methods that account for these systematic biases and uncertainties. We expect our methods to yield robust constraints on f_NL,local for both our own and future large-scale-structure investigations.
We explore the benefits of using a passively evolving population of galaxies to measure the evolution of the rate of structure growth between z=0.25 and z=0.65 by combining data from the SDSS-I/II and SDSS-III surveys. The large-scale linear bias of
a population of dynamically passive galaxies, which we select from both surveys, is easily modeled. Knowing the bias evolution breaks degeneracies inherent to other methodologies, and decreases the uncertainty in measurements of the rate of structure growth and the normalization of the galaxy power-spectrum by up to a factor of two. If we translate our measurements into a constraint on sigma_8(z=0) assuming a concordance cosmological model and General Relativity (GR), we find that using a bias model improves our uncertainty by a factor of nearly 1.5. Our results are consistent with a flat Lambda Cold Dark Matter model and with GR.
We analyze the density field of galaxies observed by the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) included in the SDSS Data Release Nine (DR9). DR9 includes spectroscopic redshifts for over 400,000 galaxies s
pread over a footprint of 3,275 deg^2. We identify, characterize, and mitigate the impact of sources of systematic uncertainty on large-scale clustering measurements, both for angular moments of the redshift-space correlation function and the spherically averaged power spectrum, P(k), in order to ensure that robust cosmological constraints will be obtained from these data. A correlation between the projected density of stars and the higher redshift (0.43 < z < 0.7) galaxy sample (the `CMASS sample) due to imaging systematics imparts a systematic error that is larger than the statistical error of the clustering measurements at scales s > 120h^-1Mpc or k < 0.01hMpc^-1. We find that these errors can be ameliorated by weighting galaxies based on their surface brightness and the local stellar density. We use mock galaxy catalogs that simulate the CMASS selection function to determine that randomly selecting galaxy redshifts in order to simulate the radial selection function of a random sample imparts the least systematic error on correlation function measurements and that this systematic error is negligible for the spherically averaged correlation function. The methods we recommend for the calculation of clustering measurements using the CMASS sample are adopted in companion papers that locate the position of the baryon acoustic oscillation feature (Anderson et al. 2012), constrain cosmological models using the full shape of the correlation function (Sanchez et al. 2012), and measure the rate of structure growth (Reid et al. 2012). (abridged)
We introduce a novel technique for empirically understanding galaxy evolution. We use empirically determined stellar evolution models to predict the past evolution of the Sloan Digital Sky Survey (SDSS-II) Luminous Red Galaxy (LRG) sample without any
a-priori assumption about galaxy evolution. By carefully contrasting the evolution of the predicted and observed number and luminosity densities we test the passive evolution scenario for galaxies of different luminosity, and determine minimum merger rates. We find that the LRG population is not purely coeval, with some of galaxies targeted at z<0.23 and at z>0.34 showing different dynamical growth than galaxies targeted throughout the sample. Our results show that the LRG population is dynamically growing, and that this growth must be dominated by the faint end. For the most luminous galaxies, we find lower minimum merger rates than required by previous studies that assume passive stellar evolution, suggesting that some of the dynamical evolution measured previously was actually due to galaxies with non-passive stellar evolution being incorrectly modelled. Our methodology can be used to identify and match coeval populations of galaxies across cosmic times, over one or more surveys.
We outline how redshift-space distortions (RSD) can be measured from the angular correlation function w({theta}), of galaxies selected from photometric surveys. The natural degeneracy between RSD and galaxy bias can be minimized by comparing results
from bins with top-hat galaxy selection in redshift, and bins based on the radial position of galaxy pair centres. This comparison can also be used to test the accuracy of the photometric redshifts. The presence of RSD will be clearly detectable with the next generation of photometric redshift surveys. We show that the Dark Energy Survey (DES) will be able to measure f(z){sigma}_8(z) to a 1{sigma} accuracy of (17 {times} b)%, using galaxies drawn from a single narrow redshift slice centered at z = 1. Here b is the linear bias, and f is the logarithmic rate of change of the linear growth rate with respect to the scale factor. Extending to measurements of w({theta}) for a series of bins of width 0.02(1 + z) over 0.5 < z < 1.4 will measure {gamma} to a 1{sigma} accuracy of 25%, given the model f = {Omega}_m(z)^{gamma}, and assuming a linear bias model that evolves such that b = 0.5 + z (and fixing other cosmological parameters). The accuracy of our analytic predictions is confirmed using mock catalogs drawn from simulations conducted by the MICE collaboration.
We present a series of colour evolution models for Luminous Red Galaxies (LRGs) in the 7th spectroscopic data release of the Sloan Digital Sky Survey (SDSS), computed using the full-spectrum fitting code VESPA on high signal-to-noise stacked spectra.
The colour-evolution models are computed as a function of colour, luminosity and redshift, and we do not a-priori assume that LRGs constitute a uniform population of galaxies in terms of stellar evolution. By computing star-formation histories from the fossil record, the measured stellar evolution of the galaxies is decoupled from the surveys selection function, which also evolves with redshift. We present these evolutionary models computed using three different sets of Stellar Population Synthesis (SPS) codes. We show that the traditional fiducial model of purely passive stellar evolution of LRGs is broadly correct, but it is not sufficient to explain the full spectral signature. We also find that higher-order corrections to this model are dependent on the SPS used, particularly when calculating the amount of recent star formation. The amount of young stars can be non-negligible in some cases, and has important implications for the interpretation of the number density of LRGs within the selection box as a function of redshift. Dust extinction, however, is more robust to the SPS modelling: extinction increases with decreasing luminosity, increasing redshift, and increasing r-i colour. We are making the colour evolution tracks publicly available at http://www.icg.port.ac.uk/~tojeiror/lrg_evolution/.
