ABSTRACT
Chiral symmetry is maximally violated in weak interactions [1], and such microscopic asymmetries in the early Universe might leave observable imprints on astrophysical scales without violating the cosmological principle. In this Letter, we propose a helicity measurement to detect primordial chiral violation. We point out that observations of halo-galaxy angular momentum directions (spins), which are frozen in during the galaxy formation process, provide a fossil chiral observable. From the clustering mode of large scale structure of the Universe, we construct a spin mode in Lagrangian space and show in simulations that it is a good probe of halo-galaxy spins. In the standard model, a strong symmetric correlation between the left and right helical components of this spin mode and galaxy spins is expected. Measurements of these correlations will be sensitive to chiral breaking, providing a direct test of chiral symmetry breaking in the early Universe.