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

What can galaxy shapes tell us about physics beyond the standard model?