A cross-bispectrum estimator for CMB-HI intensity mapping correlations

Intensity mapping of 21cm emission from neutral hydrogen promises to be a powerful probe of large-scale structure in the post-reionisation epoch. However, HI intensity mapping (IM) experiments will suffer the loss of long-wavelength line-of-sight HI modes in the foreground subtraction process. This significantly reduces HI IM cross-correlations with projected large-scale structure tracers, such as CMB secondary anisotropies. Here we propose a cross-bispectrum estimator, $B^{\bar \kappa \delta T_{21} \delta T_{21}},$ to recover the cross-correlation of the HI IM field, $\delta T_{21},$ with the CMB lensing field, $\kappa,$ constructed by correlating the position-dependent HI power spectrum with the mean overdensity traced by CMB lensing. We study the cross-bispectrum estimator in the squeezed limit and forecast its detectability based on HI IM measurements from HIRAX and CMB lensing measurements from Advanced ACT. We find that $B^{\bar \kappa \delta T_{21}\delta T_{21}},$ in combination with the HI IM and CMB lensing auto-spectra, can place sub-percent constraints on the growth rate of fluctuations, $f,$ and the small scale amplitude of fluctuations, $ \sigma_8.$ The cross-bispectrum, in combination with the auto-spectra and Planck priors, improves dark energy constraints to 0.025 on $w_0$ and 0.11 on $w_a$ for flat models. These results are robust to HI foreground removal because they derive from small-scale HI modes. The HI-CMB lensing cross-bispectrum thus provides a novel way to recover HI correlations with CMB lensing and constrain cosmological parameters at a level that is competitive with next-generation galaxy redshift surveys. As a striking example of this, we find a tight constraint of 27.8 meV (29.0 meV) on the sum of neutrino masses, while varying all redshift and standard cosmological parameters within a flat $\Lambda$CDM ($w_0w_a$CDM) model.