  We discuss the constraints imposed on the nonlinear evolution of the Large
Scale Structure (LSS) of the universe by galilean invariance, the symmetry
relevant on subhorizon scales. Using Ward identities associated to the
invariance, we derive fully nonlinear consistency relations between statistical
correlators of the density and velocity perturbations, such as the power
spectrum and the bispectrum. These relations are valid up to O (f_{NL}^2)
corrections. We then show that most of the semi-analytic methods proposed so
far to resum the perturbative expansion of the LSS dynamics fail to fulfill the
constraints imposed by galilean invariance, and are therefore susceptible to
non-physical infrared effects. Finally, we identify and discuss a
nonperturbative semi-analytical scheme which is manifestly galilean invariant
at any order of its expansion.
