Constraining the ionized gas evolution with CMB-spectroscopic survey cross-correlation

We forecast the prospective constraints on the ionized gas model fgas(z) at different evolutionary epochs via the tomographic cross-correlation between kinetic Sunyaev-Zeldovich (kSZ) effect and the reconstructed momentum field at different redshifts. The experiments we consider are the Planck and CMB Stage-4 survey for CMB and the SDSS-III for the galaxy spectroscopic survey. We calculate the tomographic cross-correlation power spectrum, and use the Fisher matrix to forecast the detectability of different fgas(z) models. We find that for constant fgas model, Planck can constrain the error of fgas (σfgas) at each redshift bin to ∼0.2, whereas four cases of CMB-S4 can achieve σfgas∼10−3. For fgas(z)=fgas,0/(1+z) model the error budget will be slightly broadened. We also investigate the model fgas(z)=fgas,0/(1+z)α. Planck is unable to constrain the index of redshift evolution, but the CMB-S4 experiments can constrain the index α to the level of σα∼0.01-0.1. The tomographic cross-correlation method will provide an accurate measurement of the ionized gas evolution at different epochs of the Universe.