During the adiabatic evolution of the universe, a constant gradient of the curvature perturbation is a gauge mode: it can be reabsorbed by performing a coordinate transformation of the background FLRW metric; this allows one to derive consistency relations among an n-point correlation function and an (n+1)-point function in the limit in which the extra momentum is soft. I will start by deriving such consistency relations in the context of single-field inflation and then show that they hold also in the later universe. The power of these relations lies in the fact that they hold non-perturbatively in the hard modes. I will then discuss the relevance of these results for testing inflation and the standard cosmological model.
