Cross bispectra and trispectra of the non-linear integrated Sachs-Wolfe
  effect and the tracer galaxy density field
  In order to investigate possibilities to measure non-Gaussian signatures of
the non-linear iSW effect, we study in this work the family of mixed bispectra
<tau^q gamma^(3-q)> and trispectra <tau^q gamma^(4-q)> between the integrated
Sachs-Wolfe (iSW) temperature perturbation tau and the galaxy over-density
gamma. We use standard Eulerian perturbation theory restricted to tree level
expansion for predicting the cosmic matter field. As expected, the spectra are
found to decrease in amplitude with increasing q. The transition scale between
linear domination and the scales, on which non-linearities take over, moves to
larger scales with increasing number of included iSW source fields q. We derive
the cumulative signal-to-noise ratios for a combination of Planck CMB data and
the galaxy sample of a Euclid-like survey. Including scales down to l_max =
1000 we find sobering values of sigma = 0.83 for the mixed bispectrum and sigma
= 0.19 in case of the trispectrum for q=1. For higher values of q the
polyspectra <tau^2 gamma> and <tau^3 gamma> are found to be far below the
detection limit.
