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One of the cornerstones of general relativity is the equivalence principle.However, the validity of the equivalence principle has only been established onsolar system scales for standard matter fields; this result cannot be assumedto hold for the non-standard matter fields that dominate the gravitationaldynamics on cosmological scales. Here we show how the equivalence principle maybe tested on cosmological scales for non-standard matter fields using the oddmultipoles of the galaxy cross-power spectrum and bispectrum. This test makesuse of the imprint on the galaxy cross-power spectrum and bispectrum by theparity-violating general relativistic deformations of the past-light cone, andassumes that galaxies can be treated as test particles that are made of baryonsand cold dark matter. This assumption leads to a non-zero galaxy-baryonrelative velocity if the equivalence principle does not hold between baryonsand dark matter. We show that the relative velocity can be constrained to beless than 28% of the galaxy velocity using the cross-power spectrum of the HIintensity mapping/H$\alpha$ galaxy survey and the bispectrum of the H$\alpha$galaxy survey.

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