Mixed three-point correlation functions of the nonlinear integrated Sachs-Wolfe effect and their detectability

In this paper I investigate the family of mixed three-point correlation functions <tau^q gamma^{3-q}>, q=0,1,2, between the integrated Sachs-Wolfe (iSW) temperature perturbation tau and the galaxy overdensity gamma as a tool for detecting the gravitational interaction of cosmic microwave background (CMB) photons with the potentials of nonlinearly evolving cosmological structures. Both the iSW-effect as well as the galaxy overdensity are derived in hyper-extended perturbation theory to second order and I emphasise the different parameter sensitivities of the linear and non-linear iSW-effect. I examine the configuration dependence of the relevant bispectra, quantify their sensitivities and discuss their degeneracies with respect to the cosmological parameters Omega_m, sigma_8, h and the dark energy equation of state parameter $w$. I give detection sigificances for combining PLANCK CMB data and the DUNE galaxy sample, by using a quadratic approximation for the likelihood with LambdaCDM as the fiducial cosmology: The combination of PLANCK with DUNE should be able to reach a cumulative signal to noise ratio of ~0.6sigma for the bispectrum <tau gamma^2> up to l=2000, where the most important noise source are the primary CMB fluctuations.