Gaussian Approximation of Peak Values in the Integrated Sachs-Wolfe
  Effect
  The accelerating expansion of the universe at recent epochs is encoded in the
cosmic microwave background: a few percent of the total temperature
fluctuations are generated by evolving gravitational potentials which trace the
large-scale structures in the universe. This signature of dark energy, the
Integrated Sachs-Wolfe Effect, has been detected by averaging temperatures in
the WMAP sky maps corresponding to the directions of superstructures in the
Sloan Digital Sky Survey data release 6. We model the maximum average peak
signal expected in the standard $\Lambda$CDM cosmological model, using Gaussian
random realizations of the microwave sky, including correlations between
different physical contributions to the temperature fluctuations and between
different redshift ranges of the evolving gravitational potentials. We find
good agreement with the mean temperature peak amplitude from previous
theoretical estimates based on large-scale structure simulations, but with
larger statistical uncertainties. We apply our simulation pipeline to four
different foreground-cleaned microwave temperature maps from Planck and WMAP
data, finding a mean temperature peak signal at previously identified sky
locations which exceeds our theoretical mean signal at a statistical
significance of about $2.5\sigma$ and which differs from a null signal at
$3.5\sigma$.
