  The shapes of galaxies trace scalar physics in the late-Universe through the
large-scale gravitational potential. Are they also sensitive to higher-spin
physics? We present a general study into the observational consequences of
vector and tensor modes in the early and late Universe, through the statistics
of cosmic shear and its higher-order generalization, flexion. Higher-spin
contributions arise from both gravitational lensing and intrinsic alignments,
and we give the leading-order correlators for each (some of which have been
previously derived), in addition to their flat-sky limits. In particular, we
find non-trivial sourcing of shear $EB$ and $BB$ spectra, depending on the
parity properties of the source. We consider two sources of vector and tensor
modes: scale-invariant primordial fluctuations and cosmic strings, forecasting
the detectability of each for upcoming surveys. Shear is found to be a powerful
probe of cosmic strings, primarily through the continual sourcing of vector
modes; flexion adds little to the constraining power except on very small
scales ($\ell\gtrsim 1000$), though it could be an intriguing probe of
as-yet-unknown rank-three tensors or halo-scale physics. Such probes could be
used to constrain new physics proposed to explain recent pulsar timing array
observations.
