Testing the equivalence principle on cosmological scales

TL;DR

This paper proposes a method to test the equivalence principle on cosmological scales by analyzing relativistic effects in large-scale structure, enabling constraints on dark matter's free-fall behavior with future surveys.

Contribution

It introduces a parametrization for deviations from Euler's equation and forecasts how upcoming surveys can constrain these deviations, providing a new test of the equivalence principle in cosmology.

Findings

Deviations from Euler's equation can be constrained to about 10% with future surveys.

Relativistic effects offer a new way to test the equivalence principle on large scales.

Standard methods like redshift-space distortions are insensitive to these deviations.

Abstract

The equivalence principle, that is one of the main pillars of general relativity, is very well tested in the Solar system; however, its validity is more uncertain on cosmological scales, or when dark matter is concerned. This article shows that relativistic effects in the large-scale structure can be used to directly test whether dark matter satisfies Euler's equation, i.e. whether its free fall is characterised by geodesic motion, just like baryons and light. After having proposed a general parametrisation for deviations from Euler's equation, we perform Fisher-matrix forecasts for future surveys like DESI and the SKA, and show that such deviations can be constrained with a precision of order 10%. Deviations from Euler's equation cannot be tested directly with standard methods like redshift-space distortions and gravitational lensing, since these observables are not sensitive to the time component of the metric. Our analysis shows therefore that relativistic effects bring new and complementary constraints to alternative theories of gravity.