Cosmological test of local position invariance from the asymmetric galaxy clustering

TL;DR

This paper proposes a novel cosmological test of local position invariance using galaxy clustering asymmetries, enabling constraints on potential violations over large cosmological scales.

Contribution

It introduces a new method to test LPI through galaxy cross-correlation asymmetries caused by gravitational redshift effects, extending tests to higher redshifts and larger scales.

Findings

Expected upper limit on LPI-violating parameter $oldsymbol{eta}$ can reach 0.03.

Upcoming surveys can constrain LPI violations at redshifts 0.1 to 1.8.

Method explores gravitational redshift effects in galaxy clustering asymmetries.

Abstract

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