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 $3.6\sigma$ confidence level~(CL), with the autocorrelation of the Planck tSZ data being measured at a $25 \sigma$ CL. The joint auto- and cross-power spectra constrain the matter density to be $\Omega_{\rm m}= 0.317^{+0.040}_{-0.031}$, the Hubble constant $H_{0}=66.5^{+2.0}_{-1.9}\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ and the rms matter density fluctuations to be $\sigma_{8}=0.730^{+0.040}_{-0.037}$ at the 68% CL. The derived large-scale structure $S_{8}$ parameter is $S_8 \equiv \sigma_{8}(\Omega_{\rm m}/0.3)^{0.5} = 0.755\pm{0.060}$. If using only the diagonal blocks of covariance matrices, the Hubble constant becomes $H_{0}=69.7^{+2.0}_{-1.5}\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$. In addition, we obtain the constraint of the product of the gas bias, gas temperature, and density as $b_{\rm gas} \left(T_{\rm e}/(0.1\,{\rm keV}) \right ) \left(\bar{n}_{\rm e}/1\,{\rm m}^{-3} \right) = 3.09^{+0.320}_{-0.380}$. We find that this constraint leads to an estimate on the electron temperature today as $T_{\rm e}=(2.40^{+0.250}_{-0.300}) \times 10^{6} \,{\rm K}$, 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.