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The local position invariance (LPI) is one of the three major pillars ofEinstein equivalence principle, ensuring the space-time independence on theoutcomes of local experiments. The LPI has been tested by measuring thegravitational redshift effect in various depths of gravitational potentials. Wepropose a new cosmological test of the LPI by observing the asymmetry in thecross-correlation function between different types of galaxies, whichpredominantly arises from the gravitational redshift effect induced by thegravitational potential of halos at which the galaxies reside. We show that theongoing and upcoming galaxy surveys can give a fruitful constraint on theLPI-violating parameter, $\alpha$, at distant universes (redshift$z\sim0.1-1.8$) over the cosmological scales (separation $s\sim5-10\, {\rmMpc}/h$) that have not yet been explored, finding that the expected upper limiton $\alpha$ can reach $0.03$.

Cosmological test of local position invariance from the asymmetric galaxy clustering