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

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-Lemaître-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.

5 pages, 3 figures. Submitted