Cross Correlation between the Thermal Sunyaev–Zeldovich Effect and the Integrated Sachs–Wolfe Effect

Abstract

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 σ confidence level (CL), with the autocorrelation of the Planck tSZ data being measured at a 25 σ 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 S _8 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.

Keywords

• Large-scale structure of the universe