  One of the cornerstones of general relativity is the equivalence principle.
However, the validity of the equivalence principle has only been established on
solar system scales for standard matter fields; this result cannot be assumed
to hold for the non-standard matter fields that dominate the gravitational
dynamics on cosmological scales. Here we show how the equivalence principle may
be tested on cosmological scales for non-standard matter fields using the odd
multipoles of the galaxy cross-power spectrum and bispectrum. This test makes
use of the imprint on the galaxy cross-power spectrum and bispectrum by the
parity-violating general relativistic deformations of the past-light cone, and
assumes that galaxies can be treated as test particles that are made of baryons
and cold dark matter. This assumption leads to a non-zero galaxy-baryon
relative velocity if the equivalence principle does not hold between baryons
and dark matter. We show that the relative velocity can be constrained to be
less than 28% of the galaxy velocity using the cross-power spectrum of the HI
intensity mapping/H$\alpha$ galaxy survey and the bispectrum of the H$\alpha$
galaxy survey.
