We forecast the prospective constraints on the ionized gas model f _ { gas } ( 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 f _ { gas } ( z ) models .
We find that for constant f _ { gas } model , Planck can constrain the error of f _ { gas } ( \sigma _ { f _ { gas } } ) at each redshift bin to \sim 0.2 , whereas four cases of CMB-S4 can achieve \sigma _ { f _ { gas } } \sim 10 ^ { -3 } .
For f _ { gas } ( z ) = f _ { gas, 0 } / ( 1 + z ) model the error budget will be slightly broadened .
We also investigate the model f _ { gas } ( z ) = f _ { gas, 0 } / ( 1 + z ) ^ { \alpha } . Planck is unable to constrain the index of redshift evolution , but the CMB-S4 experiments can constrain the index \alpha to the level of \sigma _ { \alpha } \sim 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 .