The Integrated Sachs Wolfe effect and its cross-correlation with the Large Scale Structure distribution of galaxies: exploring higher-order correlations.

Anisotropies of the Cosmic Microwave Background (CMB) are conventionally treated linearly under the hypothesis of complete Gaussianity, which allows them to be fully described by their power spectrum. However, this may not be a complete description. We give a brief introduction to CMB anisotropies, highlighting the role of their study in modern cosmology, before considering whether measurable CMB non-Gaussianities exist, their statistical description in terms of the bispectrum (i.e. the Fourier counterpart of the 3-point correlation function), and what physical information could be gained by their analysis. We focus in particular on the integrated Sachs-Wolfe (ISW) effect, the dominant CMB anisotropy contribution on large scales, and the non-Gaussianity generated by its nonlinear component, the Rees-Sciama effect. As the ISW effect was recently detected through its cross-correlation with the distribution of the Large Scale Structure (LSS), we give a brief overview of the current status of galaxy surveys and LSS mapping, before considering the possibility of detecting the non-Gaussian signature of the Rees-Sciama effect by means of a fully relativistic analysis, up to second order in the cosmological perturbations, of the cross ISW-Galaxy overdensity bispectra on ultra-large scales. Finally, after an examination of the theoretical achievements in the field of second-order, fully relativistic description of both CMB and LSS anisotropies, we write down the expressions for such bispectra in our conclusions