  The cosmological dynamics of gravitational clustering satisfies an
approximate invariance with respect to the cosmological parameters that is
often used to simplify analytical computations. We describe how this
approximate symmetry gives rise to angular averaged consistency relations for
the matter density correlations. This allows one to write the $(\ell+n)$
density correlation, with $\ell$ large-scale linear wave numbers that are
integrated over angles, and $n$ fixed small-scale nonlinear wave numbers, in
terms of the small-scale $n$-point density correlation and $\ell$ prefactors
that involve the linear power spectra at the large-scale wave numbers. These
relations, which do not vanish for equal-time statistics, go beyond the already
known kinematic consistency relations. They could be used to detect primordial
non-Gaussianities, modifications of gravity, limitations of galaxy biasing
schemes, or to help designing analytical models of gravitational clustering.
