Comparison of the Large Scale Clustering in the APM and the EDSGC Galaxy Surveys

Clustering statistics are compared in the Automatic Plate Machine (APM) and the Edinburgh/Durham Southern Galaxy Catalogue (EDSGC) angular galaxy surveys. Both surveys were independently constructed from scans of the same adjacent UK IIIa--J Schmidt photographic plates with the APM and COSMOS microdensitometers, respectively. The comparison of these catalogs is a rare practical opportunity to study systematic errors, which cannot be achieved via simulations or theoretical methods. On intermediate scales, $0.1^\circ < \theta < 0.5^\circ$, we find good agreement for the cumulants or reduced moments of counts in cells up to sixth order. On larger scales there is a small disagreement due to edge effects in the EDSGC, which covers a smaller area. On smaller scales, we find a significant disagreement that can only be attributed to differences in the construction of the surveys, most likely the dissimilar deblending of crowded fields. The overall agreement of the APM and EDSGC is encouraging, and shows that the results for intermediate scales should be fairly robust. On the other hand, the systematic deviations found at small scales are significant in a regime, where comparison with theory and simulations is possible. This is an important fact to bear in mind when planning the construction of future digitized galaxy catalogs.Comment: 4 pages with 3 figures included. Submitted for MNRAS 'pink pages

2-Point Moments in Cosmological Large Scale Structure: I. Theory and Comparison with Simulations

We present new perturbation theory (PT) predictions in the Spherical Collapse (SC) model for the 2-point moments of the large-scale distribution of dark matter density in the universe. We assume that these fluctuations grow under gravity from small Gaussian initial conditions. These predictions are compared with numerical simulations and with previous PT results to assess their domain of validity. We find that the SC model provides in practice a more accurate description of 2-point moments than previous tree-level PT calculations. The agreement with simulations is excellent for a wide range of scales (5-50 Mpc/h) and fluctuations amplitudes (0.02-2 variance). When normalized to unit variance these results are independent of the cosmological parameters and of the initial amplitude of fluctuations. The 2-point moments provide a convenient tool to study the statistical properties of gravitational clustering for fairly non-linear scales and complicated survey geometries, such as those probing the clustering of the Ly-alpha forest. In this context, the perturbative SC predictions presented here, provide a simple and novel way to test the gravitational instability paradigm.Comment: 10 LaTeX pages, 9 figs, submitted to MNRA

The Local Bias Model in the Large Scale Halo Distribution

We explore the biasing in the clustering statistics of halos as compared to dark matter (DM) in simulations. We look at the second and third order statistics at large scales of the (intermediate) MICEL1536 simulation and also measure directly the local bias relation h = f({\delta}) between DM fluctuations, {\delta}, smoothed over a top-hat radius Rs at a point in the simulation and its corresponding tracer h (i.e. halos) at the same point. This local relation can be Taylor expanded to define a linear (b1) and non-linear (b2) bias parameters. The values of b1 and b2 in the simulation vary with Rs approaching a constant value around Rs > 30 - 60 Mpc/h. We use the local relation to predict the clustering of the tracer in terms of the one of DM. This prediction works very well (about percent level) for the halo 2-point correlation {\xi}(r_12) for r_12 > 15 Mpc/h, but only when we use the biasing values that we found at very large smoothing radius Rs > 30 - 60 Mpc/h. We find no effect from stochastic or next to leading order terms in the f({\delta}) expansion. But we do find some discrepancies in the 3-point function that needs further understanding. We also look at the clustering of the smoothed moments, the variance and skewness which are volume average correlations and therefore include clustering from smaller scales. In this case, we find that both next to leading order and discreetness corrections (to the local model) are needed at the 10 - 20% level. Shot-noise can be corrected with a term {\sigma}e^2/n where {\sigma}e^2 < 1, i.e., always smaller than the Poisson correction. We also compare these results with the peak-background split predictions from the measured halo mass function. We find 5-10% systematic (and similar statistical) errors in the mass estimation when we use the halo model biasing predictions to calibrate the mass.Comment: Accepted in MNRAS. Compared to first version, the paper has been completely reorganised. New figures and content adde

Large-Scale Structure of the Universe and Cosmological Perturbation Theory

We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver

Clustering of photometric luminous red galaxies I : Growth of Structure and Baryon Acoustic Feature

The possibility of measuring redshift space (RSD) distortions using photometric data have been recently highlighted. This effect complements and significantly alters the detectability of baryon acoustic oscillations (BAO) in photometric surveys. In this paper we present measurements of the angular correlation function of luminous red galaxies (LRGs) in the photometric catalog of the final data release (DR7) of the Sloan Digital Sky Survey II (SDSS). The sample compromise ~ 1.5 x 10^6 LRGs distributed in 0.45 < z < 0.65, with a characteristic photometric error of ~ 0.05. Our measured correlation centered at z=0.55 is in very good agreement with predictions from standard LCDM in a broad range of angular scales, $0.5^\circ < \theta < 6^\circ$. We find that the growth of structure can indeed be robustly measured, with errors matching expectations. The velocity growth rate is recovered as $f \sigma_8 = 0.53 \pm 0.42$ when no prior is imposed on the growth factor and the background geometry follows a LCDM model with WMAP7+SNIa priors. This is compatible with the corresponding General Relativity (GR) prediction $f \sigma_8 = 0.45$ for our fiducial cosmology. If we adopt a parametrization such that $f=\Omega ^\gamma_m(z)$, with $\gamma \approx 0.55$ in GR, and combine our $f\sigma_8$ measurement with the corresponding ones from spectroscopic LRGs at lower redshifts we obtain $\gamma=0.54 \pm 0.17$. In addition we find evidence for the presence of the baryon acoustic feature matching the amplitude, location and shape of LCDM predictions. The photometric BAO feature is detected with 98 % confidence level at z=0.55.Comment: 16 pages, 19 figures, minor changes to text to match accepted version by MNRA