Testing the equivalence principle on cosmological scales using the odd
  multipoles of galaxy cross-power spectrum and bispectrum
  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.
