Testing the equivalence principle on cosmological scales using the odd multipoles of galaxy cross-power spectrum and bispectrum
Obinna Umeh, Kazuya Koyama, Robert Crittenden
Abstract
One of the cornerstones of general relativity is the equivalence principle. However, \nthe validity of the equivalence principle has only been established on solar system scales for \nstandard matter fields; this result cannot be assumed to hold for the non-standard matter \nfields that dominate the gravitational dynamics on cosmological scales. Here we show how \nthe equivalence principle may be tested on cosmological scales for non-standard matter fields \nusing the odd multipoles of the galaxy cross-power spectrum and bispectrum. This test makes \nuse of the imprint on the galaxy cross-power spectrum and bispectrum by the parity-violating \ngeneral relativistic deformations of the past-light cone, and assumes that galaxies can be \ntreated as test particles that are made of baryons and cold dark matter. This assumption \nleads to a non-zero galaxy-baryon relative velocity if the equivalence principle does not hold \nbetween baryons and dark matter. We show that the relative velocity can be constrained to \nbe less than 28% of the galaxy velocity using the cross-power spectrum of the HI intensity \nmapping/Hα galaxy survey and the bispectrum of the Hα galaxy survey.