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We measure the matter probability distribution function (PDF) via counts incells in a volume limited subsample of the Sloan Digital Sky Survey LuminousRed Galaxy Catalog on scales from $30 h^{-1}$Mpc to $150 h^{-1}$Mpc andestimate the linear Integrated Sachs--Wolfe effect produced by supervoids andsuperclusters 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 finitevolume, survey shape and redshift distortion. We compare our measurement to theprediction of $\Lambda$CDM with linear bias and find a good agreement. We usethe moments to approximate the tail of the PDF with analytic functions. Asimple Gaussian model for the superstructures appears to be consistent with theclaim by Granett et al. that density fluctuations on $100 h^{-1}$Mpc scalesproduce hot and cold spots with $\Delta T \approx 10\mu K$ on the cosmicmicrowave background.

Cosmological Density Fluctuations on 100Mpc Scales and their ISW Effect