Galilean invariance and the consistency relation for the nonlinear squeezed bispectrum of large scale structure

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(fNL2) 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.