Cosmic statistics on linear scales

Abstract

We use the formalism of Szapudi (2004) to derive full explicit expressions for the linear two-point correlation function, including redshift space distortions and large angle effects. We take into account a non-perturbative geometric term in the Jacobian, which is still linear in terms of the dynamics. This term had been identified previously (Kaiser, 1987; Hamilton and Culhane, 1996), but has been neglected in all subsequent explicit calculations of the linear redshift space two-point correlation function. Our results represent a significant correction to previous explicit expressions and are in excellent agreement with our measurements in the Hubble Volume Simulation. We measure the matter probability distribution function (PDF) via counts in cells in a volume limited subsample of the Sloan Digital Sky Survey (SDSS) Luminous Red Galaxy Catalog on scales from 30 h−1Mpc to 150 h−1Mpc and estimate the linear integrated Sachs--Wolfe (ISW) effect produced by supervoids and superclusters in the tail of the PDF. We characterize the PDF by the variance, S3, and S4, and study in simulations the systematic effects due to finite volume, survey shape and redshift distortion. We compare our measurement to the prediction of CDM with linear bias and find a good agreement. We use the moments to approximate the tail of the PDF with analytic functions. A simple Gaussian model for the superstructures appears to be consistent with the claim by Granett et al. (2008) that density fluctuations on 100 h−1Mpc scales produce hot and cold spots with T ≈ 10μK on the cosmic microwave background. We calculate the full density and ISW profiles of spherical superstructures. We find that the Gaussian assumptions capable of describing N-body simulations and simulated ISW maps remarkably well on large scales. We construct an ISW map based on locations of superstructures identified previously in the SDSS Luminous Red Galaxy sample. A matched filter analysis of the cosmic microwave background confirms a signal at the 3.2 − σ confidence level and estimates the radius of the underlying structures to be 55 ± 28h−1Mpc. The amplitude of the signal, however, is 2 − σ higher than CDM predictions.