A linear relation between galaxy-lensing cross-correlations to test the cosmological principle model-independently

TL;DR

This paper introduces a model-independent test of the cosmological principle by identifying a linear relation in galaxy-lensing cross-correlations that, if violated, indicates deviations from the FLRW metric.

Contribution

The authors discover a linear relation in galaxy-lensing cross-correlations that serves as a direct, model-independent test of the cosmological principle and FLRW metric.

Findings

Stage IV galaxy surveys can test the linear relation.

CMB-S4 experiments can perform stringent tests.

Violation indicates breakdown of the cosmological principle.

Abstract

We discover a linear relation between two sets of galaxy-lensing cross-correlations. This linear relation holds, as long as light follows the geodesic and the metric is Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW). Violation of the cosmological principle (and equivalently the FLRW metric) will break this linear relation. Therefore it provides a powerful test of the cosmological principle, based on direct observables and relied on no specific cosmological models. We demonstrate that stage IV galaxy surveys and CMB-S4 experiments will be able to test this linear relation stringently and therefore test the cosmological principle robustly.