Cross-correlations between mm-wave line-intensity mapping and weak
  lensing surveys: preliminary consideration of long-term prospects
  The field of millimetre-wave line-intensity mapping (LIM) is seeing increased
experimental activity with pathfinder surveys already deployed or deploying in
the next few years, making spectroscopic measurements of unresolved atomic and
molecular line emission tracing the large-scale structure of the Universe. The
next decade will also see the Rubin Observatory Legacy Survey of Space and Time
(LSST) undertake a photometric galaxy survey programme of unprecedented scope,
including measurements of cosmic shear exploiting weak gravitational lensing
(WL) of background galaxies to map projected large-scale structure. We consider
prospects for detecting angular cross power spectra between non-tomographic
cosmic shear and mm-wave LIM surveys that measure emission from CO lines at
$z=0.5$-$1$. We forecast that once the LSST Year 10 WL dataset is available, a
future LIM experiment, conceivably deployed in the next 10-15 years, would
enable such a cross-correlation detection with an overall signal-to-noise ratio
of $50$, although the current pathfinder generation of CO/[C II] surveys are
more likely to achieve a marginal $2\sigma$ detection against an earlier-stage
LSST WL dataset. The signal has modest astrophysical constraining power
yielding competitive constraints on cosmic molecular gas density at
$z\lesssim1$, and degeneracies between astrophysical parameters and the
intrinsic alignment amplitude mean that external information on either one
could allow the cross-correlation analysis to significantly improve its
constraints on the other.
