Squared temperature-temperature power spectrum as a probe of the CMB bispectrum - art. no. 043516

It is now well known that mode-coupling effects associated with certain sec ondary effects generate higher order correlations in cosmic microwave backg round (CMB) temperature anisotropies, beyond the two-point function. In ord er to extract such a non-Gaussian signal at the three-point level, we sugge st a two-point statistic in the form of an angular power spectrum involving correlations between squared temperature and temperature anisotropies. Thi s power spectrum contains compressed information from the bispectrum and ca n be easily measured in data with the same techniques that have been consid ered for the measurement of the usual temperature-temperature anisotropy po wer spectrum. We study the proposed power spectrum resulting from the non-G aussian signal generated by correlations involved with gravitational lensin g angular deflections in CMB and the Sunyaev-Zel'dovich (SZ) effect due to large scale pressure fluctuations. Using the Planck frequency cleaned CMB a nd SZ maps, the CMB2-SZ power spectrum provides a direct estimate of the cr oss-power between lensing angular deflections and the SZ effect. Through an optimal filter applied to the squared CMB map, the proposed statistic allo ws one to obtain all information from the lensing-SZ bispectrum. The observ ational measurement of the lensing-SZ cross-correlation is useful to unders tand the relation between large scale structure pressure and dark matter fl uctuations.