Single-Field Consistency Relations of Large Scale Structure. Part III:
  Test of the Equivalence Principle
  The recently derived consistency relations for Large Scale Structure do not
hold if the Equivalence Principle (EP) is violated. We show it explicitly in a
toy model with two fluids, one of which is coupled to a fifth force. We explore
the constraints that galaxy surveys can set on EP violation looking at the
squeezed limit of the 3-point function involving two populations of objects. We
find that one can explore EP violations of order 10^{-3} - 10^{-4} on
cosmological scales. Chameleon models are already very constrained by the
requirement of screening within the Solar System and only a very tiny region of
the parameter space can be explored with this method. We show that no violation
of the consistency relations is expected in Galileon models.
