  The B-(curl-)mode of the correlation of galaxy ellipticities (shear) can be
used to detect a stochastic gravitational wave background, such as that
predicted by inflation. In this paper, we derive the tensor mode contributions
to shear from both gravitational lensing and intrinsic alignments, using the
gauge-invariant, full-sky results of arXiv:1204.3625. We find that the
intrinsic alignment contribution, calculated using the linear alignment model,
is larger than the lensing contribution by an order of magnitude or more, if
the alignment strength for tensor modes is of the same order as for scalar
modes. This contribution also extends to higher multipoles. These results make
the prospects for probing tensor modes using galaxy surveys less pessimistic
than previously thought, though still very challenging.
