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

Understand

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.