Testing local position invariance with odd multipoles of galaxy clustering statistics

TL;DR

This paper explores how higher-order odd multipoles in galaxy clustering, specifically the octupole, can improve constraints on local position invariance, a key aspect of the Einstein equivalence principle, using upcoming galaxy survey data.

Contribution

It extends previous work by including the octupole moment in the analysis, demonstrating improved constraints on LPI violation parameters from galaxy surveys.

Findings

Combining dipole and octupole moments enhances LPI constraints.

Larger scale analysis (higher s_min) yields better improvements.

Higher-order multipoles provide a more robust test of the EEP.

Abstract

We investigate cosmological constraints on local position invariance (LPI), a key aspect of the Einstein equivalence principle (EEP), through asymmetric galaxy clustering. The LPI asserts that the outcomes of the non-gravitational experiments are identical regardless of location in spacetime and has been tested through measurements of the gravitational redshift effect. Therefore, measuring the gravitational redshift effect encoded in galaxy clustering provides a powerful and novel cosmological probe of the LPI. Recent work by Saga et al. proposed its validation using the cross-correlation function between distinct galaxy samples, but their analysis focused solely on the dipole moment. In this paper, we extend their work by further analyzing a higher-order odd multipole moment, the octupole moment, in the constraints on the LPI-violating parameter, $\alpha$, expected from galaxy surveys such as Dark Energy Spectroscopic Instrument, Euclid space telescope, Subaru Prime Focus Spectrograph, and Square Kilometre Array. We demonstrate that combining the octupole and dipole moments significantly improves the constraints, particularly when the analysis is restricted to larger scales, characterized by a large minimum separation $s_{\rm min}$. For a conservative setup with $s_{\rm min}=15 {\rm Mpc}/h$, we find an average improvement of 11$\%$ compared to using the dipole moment alone. Our results highlight the importance of higher-order multipoles in constraining $\alpha$, providing a more robust approach to testing the EEP on cosmological scales.