Cosmological test of local position invariance from the asymmetric galaxy clustering

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 $z\sim 0.1-1.8$) over the cosmological scales (separation $s\sim 5-10\mathrm{Mpc}/h$) that have not yet been explored, finding that the expected upper limit on $\alpha$ can reach $0.03$.

10 pages, 4 figures

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• Euclid: Relativistic effects in the dipole of the 2-point correlation function
• Relativistic imprints on dispersion measure space distortions
• Doppler bias: impact of peculiar velocities on color selection and the large scale structure of galaxy surveys
• Detecting Relativistic Doppler in Galaxy Clustering with Tailored Galaxy Samples
• Testing local position invariance with odd multipoles of galaxy clustering statistics
• Gravitational redshift from large-scale structure: nonlinearities, antisymmetries, and the dipole