HI Intensity Mapping cross-correlation with thermal SZ fluctuations: forecasted cosmological parameters estimation for FAST and Planck

The 21 cm emission from neutral hydrogen surveys holds great potential as a valuable method for exploring the large-scale structure of the Universe. In this paper, we forecast for the cross-correlation between the Thermal Sunyaev-Zel'dovich (SZ) fluctuations as probed by the Planck satellite, and fluctuations in the HI brightness temperature as probed by the ground-based Five-hundred-meter Aperture Spherical Telescope (FAST), to trace the connection between galaxy clusters and the HI large-scale structure. Assuming that the measurement is limited by instrumental noise rather than by foreground, we estimate the potential detectability of the cross-correlation signal and their improvement in the measurement of the HI cosmic density, the hydrostatic mass bias parameter, and the universal pressure profile (UPP) parameters. We obtain a constraint on the cosmic neutral hydrogen density parameter significantly to $\sigma(\Omega_{\rm HI}) = 1.0 \times 10^{-6}$. We also find that the average halo masses contributing to the ${{\rm HI}-y}$ cross-power spectrum in the one-halo regime is $\sim 1.5\times 10^{14} M_{\odot}$. Our results also show that the HI-SZ cross-correlation has great potential to probe the distribution of neutral hydrogen (HI) within halos at low redshift.