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

TL;DR

This paper explores mixed three-point correlation functions involving the ISW effect and galaxy overdensity to detect gravitational interactions in cosmology, analyzing their sensitivities and potential detectability with future data.

Contribution

It introduces a detailed theoretical framework for mixed three-point functions involving the ISW effect and galaxy overdensity, assessing their detectability with upcoming surveys.

Findings

Sensitivity of bispectra to cosmological parameters analyzed

Detection significance estimated for PLANCK and DUNE data

Degeneracies with cosmological parameters discussed

Abstract

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.