Estimating the weak-lensing rotation signal in radio cosmic shear
  surveys
  Weak lensing has become an increasingly important tool in cosmology and the
use of galaxy shapes to measure cosmic shear has become routine. The
weak-lensing distortion tensor contains two other effects in addition to the
two components of shear: the convergence and rotation. The rotation mode is not
measurable using the standard cosmic shear estimators based on galaxy shapes,
as there is no information on the original shapes of the images before they
were lensed. Due to this, no estimator has been proposed for the rotation mode
in cosmological weak-lensing surveys, and the rotation mode has never been
constrained. Here, we derive an estimator for this quantity, which is based on
the use of radio polarisation measurements of the intrinsic position angles of
galaxies. The rotation mode can be sourced by physics beyond $\Lambda$CDM, and
also offers the chance to perform consistency checks of $\Lambda$CDM and of
weak-lensing surveys themselves. We present simulations of this estimator and
show that, for the pedagogical example of cosmic string spectra, this estimator
could detect a signal that is consistent with the constraints from Planck. We
examine the connection between the rotation mode and the shear $B$-modes and
thus how this estimator could help control systematics in future radio
weak-lensing surveys.
