The weak equivalence principle is one of the cornerstone of general relativity. Its validity has been tested with impressive precision in the Solar System, with experiments involving baryonic matter and light. However, on cosmological scales and when dark matter is concerned, the validity of this principle is still unknown. In this paper we construct a null test that probes the validity of the equivalence principle for dark matter. Our test has the strong advantage that it can be applied on data without relying on any modelling of the theory of gravity. It involves a combination of redshift-space distortions and relativistic effects in the galaxy number-count fluctuation, that vanishes if and only if the equivalence principle holds. We show that the null test is very insensitive to typical uncertainties in other cosmological parameters, including the magnification bias parameter, and to non-linear effects, making this a robust null test for modified gravity.

中文翻译：

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在星系调查中使用相对论效应对等效原理进行零测试

弱等效原理是广义相对论的基石之一。它的有效性已经在太阳系中以令人印象深刻的精度进行了测试，实验涉及重子物质和光。然而，在宇宙学尺度和暗物质方面，这一原理的有效性仍然未知。在本文中，我们构建了一个零测试，探讨暗物质等效原理的有效性。我们的测试具有强大的优势，它可以在不依赖任何引力理论模型的情况下应用于数据。它涉及红移空间扭曲和星系数量波动中的相对论效应的组合，当且仅当等效原理成立时，它才会消失。我们表明，零测试对其他宇宙学参数的典型不确定性非常不敏感，