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