2024ApJS..270...16I

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 ${{\rm{\Omega }}}_{{\rm{m}}}={0.317}_{-0.031}^{+0.040}$, the Hubble constant to be ${H}_{0}={66.5}_{-1.9}^{+2.0}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$, and the rms matter density fluctuations to be ${\sigma }_{8}={0.730}_{-0.037}^{+0.040}$ at the 68% CL. The derived large-scale structure S₈ parameter is ${S}_{8}\equiv {\sigma }_{8}{({{\rm{\Omega }}}_{{\rm{m}}}/0.3)}^{0.5}=0.755\pm 0.060$. If using only the diagonal blocks of covariance matrices, the Hubble constant becomes ${H}_{0}={69.7}_{-1.5}^{+2.0}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$. In addition, we obtain the constraint of the product of the gas bias, gas temperature, and density as ${b}_{\mathrm{gas}}\left({T}_{{\rm{e}}}/(0.1\,\mathrm{keV})\right)\left({\bar{n}}_{{\rm{e}}}/1\,{{\rm{m}}}^{-3}\right)={3.09}_{-0.380}^{+0.320}$. We find that this constraint leads to an estimate on the electron temperature today as ${T}_{{\rm{e}}}=({2.40}_{-0.300}^{+0.250})\times {10}^{6}\,{\rm{K}}$, 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.