Cross-correlation between the thermal Sunyaev-Zeldovich effect and the Integrated Sachs-Wolfe effect

We present a joint cosmological analysis of the power spectra measurement of the Planck Compton parameter and the integrated Sachs-Wolfe (ISW) maps. We detect the statistical correlation between the Planck thermal Sunyaev-Zeldovich (tSZ) map and ISW data with a significance of a 3.6σ confidence level (CL), with the autocorrelation of the Planck tSZ data being measured at a 25σ CL. The joint auto- and cross-power spectra constrain the matter density to be Ω m = 0.317 − 0.031 + 0.040 , the Hubble constant to be H 0 = 66.5 − 1.9 + 2.0 km s − 1 Mpc − 1 , and the rms matter density fluctuations to be σ 8 = 0.730 − 0.037 + 0.040 at the 68% CL. The derived large-scale structure S ₈ parameter is S 8 ≡ σ 8 ( Ω m / 0.3 ) 0.5 = 0.755 ± 0.060 . If using only the diagonal blocks of covariance matrices, the Hubble constant becomes H 0 = 69.7 − 1.5 + 2.0 km s − 1 Mpc − 1 . In addition, we obtain the constraint of the product of the gas bias, gas temperature, and density as b gas T e / ( 0.1 keV ) n ¯ e / 1 m − 3 = 3.09 − 0.380 + 0.320 . We find that this constraint leads to an estimate on the electron temperature today as T e = ( 2.40 − 0.300 + 0.250 ) × 10 6 K , consistent with the expected temperature of the warm-hot intergalactic medium. Our studies show that the ISW-tSZ cross correlation is capable of probing the properties of the large-scale diffuse gas.