Kinematic consistency relations of large-scale structures
  We describe how the kinematic consistency relations satisfied by density
correlations of the large-scale structures of the Universe can be derived
within the usual Newtonian framework. These relations express a kinematic
effect and show how the $(\ell+n)$-density correlation factors in terms of the
$n$-point correlation and $\ell$ linear power spectrum factors, in the limit
where the $\ell$ soft wave numbers become linear and much smaller than the $n$
other wave numbers. We describe how these relations extend to multifluid cases.
In the standard cosmology, these consistency relations derive from the
equivalence principle. A detection of their violation would indicate
non-Gaussian initial conditions, non-negligible decaying modes, or a
modification of gravity that does not converge to General Relativity on large
scales.
