Title: 2 points statistics for week lensing and intensity maps
One of the most interesting measurements of the 2020s cosmological experiments is the intensity map of neutral hydrogen HI. While it has lower angular resolution than the optical and infrared surveys, it has better radial solution than those surveys. The cross-correlation between HI intensity map and other tracers should provide the complement to other well known observations. The major concern about this technique is its dimmer brightness temperature than foreground signals. Hence, the foreground removal is a major concern especially when measure the cross correlation with other cosmological fields. Here we explore the potential of HI and lensing convergence (K) cross correlation. In this study, 35 realisations of N-body simulations were utilised. We find that by cross correlating the intensity map and lensing, we can reduce the impact of broad frequency bins in the intensity map on the power spectra. The foreground removal moderately changes the power spectra. It reduces the signal by factor Aclean in every scales. We further illustrate the possibility of cosmological constraint by using the 2-point functions. The results show that in other to constrain cosmological parameters to sufficient level. The multi-redshift surveys of HI are required in order to break the degeneracies of parameters. When taking the HI bias into account, the finding suggests that a linear evolution model of HI bias is effective enough to constrain cosmological parameters.