Weak lensing induced by second-order vector mode
  The vector mode of cosmological perturbation theory imprints characteristic
signals on the weak lensing signals such as curl- and B-modes which are never
imprinted by the scalar mode. However, the vector mode is neglected in the
standard first-order cosmological perturbation theory since it only has a
decaying mode. This situation changes if the cosmological perturbation theory
is expanded up to second order. The second-order vector and tensor modes are
inevitably induced by the product of the first-order scalar modes. We study the
effect of the second-order vector mode on the weak lensing curl- and B-modes.
We find that the curl-mode induced by the second-order vector mode is
comparable to that induced by the primordial gravitational waves with the
tensor-to-scalar ratio $r = 0.1$ at $\ell \approx 200$. In this case, the
curl-mode induced by the second-order vector mode dominates at $\ell > 200$.
Furthermore, the B-mode cosmic shear induced by the second-order vector mode
dominates on almost all scales. However, we find that the observational
signatures of the second-order vector and tensor modes cannot exceed the
expected noise of ongoing and upcoming weak lensing measurements. We conclude
that the curl- and B-modes induced by the second-order vector and tensor modes
are unlikely to be detected in future experiments.
