Detectability of CMB Weak Lensing and HI Cross Correlation and
  constraints on cosmological parameters
  Neutral hydrogen (H$_{\rm I}$) intensity mapping is capable of measuring
redshift evolution of H$_{\rm I}$ density parameter $\Omega_{\rm H_{\rm I}}$,
which is an important parameter to understand structure formation in the
post-reionization epoch. Future H$_{\rm I}$ observation with Square Kilometre
Array (SKA) can significantly improve constraints on the parameter. However,
the observation of H$_{\rm I}$ suffers from the contamination from extremely
bright foreground emissions, and it is necessary to consider a signal
validation method complementary to the measurement of H$_{\rm I}$ auto power
spectrum. In this work, we propose to take a cross correlation between a
21cm-line intensity map and a convergence map reconstructed from observation of
the cosmic microwave background by Planck and estimate expected ideal
constraints on cosmological parametersby ignoring the foreground contamination.
We find that the SKA1-mid operated in single-dish mode has a sufficient
capability to detect the cross correlation on the large scales. Further, by
Fisher analysis assuming a constant linear bias of H$_{\rm I}$, $b$, and
SKA1-mid observation of 1,000 hours for each of Band 1 and 2, we show that
$\Omega_{\rm H_{\rm I}} b$ can be constrained with a precision of $6-13\%$ at a
wide range of redshifts of $0.0<z<2.0$, if we fix other cosmological parameters
(density parameter of cold dark matter, $\Omega_{\rm c} h^{2}$, spectral index
of primordial fluctuations, $n_s$, and Hubble constant, $H_0$) using values
from the Planck observations. On the other hand, small-scale measurements with
interferometer mode of SKA1-mid will not have a significant impact on
constraining the parameters with 1,000 hours of observation time for each of
Band 1 and 2, due to the limited resolution of the CMB lensing of Planck.
