ISW Imprint of Superstructures on Linear Scales

We build a model for the density and integrated Sachs-Wolfe (ISW) profile of supervoid and supercluster structures. Our model assumes that fluctuations evolve linearly from an initial Gaussian random field. We find these 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 $3.2-\sigma$ confidence level and estimates the radius of the underlying structures to be $55\pm 28h^{-1}$Mpc. The amplitude of the signal, however, is $2-\sigma$ higher than $\mathrm{\Lambda }$CDM predictions.