A null test of the equivalence principle using relativistic effects in galaxy surveys

Abstract

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.

30 pages, 7 figures; v2 matches the version published in JCAP

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• Wide-angle effects in the galaxy bispectrum
• Testing the equivalence principle across the Universe: a model-independent approach with galaxy multi-tracing
• Hubble tension as a window on the gravitation of the dark matter sector: Exploration of a family of models
• Relativistic distortions in galaxy density-ellipticity correlations: gravitational redshift and peculiar velocity effects
• Cosmological test of local position invariance from the asymmetric galaxy clustering
• Using relativistic effects in large-scale structure to constrain astrophysical properties of galaxy populations
• Model-Independent Test for Gravity using Intensity Mapping and Galaxy Clustering
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• Doppler bias: impact of peculiar velocities on color selection and the large scale structure of galaxy surveys
• Gravitational Redshift from Galaxy Clusters -- a Relativistic Approach
• Testing local position invariance with odd multipoles of galaxy clustering statistics