Cosmological Density Fluctuations on 100Mpc Scales and their ISW Effect

We measure the matter probability distribution function (PDF) via counts in cells in a volume limited subsample of the Sloan Digital Sky Survey Luminous Red Galaxy Catalog on scales from $30h^{-1}$Mpc to $150h^{-1}$Mpc and estimate the linear Integrated Sachs–Wolfe effect produced by supervoids and superclusters in the tail of the PDF. We characterize the PDF by the variance, $S_3$, and $S_4$, and study in simulations the systematic effects due to finite volume, survey shape and redshift distortion. We compare our measurement to the prediction of $\mathrm{\Lambda }$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. that density fluctuations on $100h^{-1}$Mpc scales produce hot and cold spots with $\mathrm{\Delta }T\approx 10\mu K$ on the cosmic microwave background.