An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology

Understand

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate (N+1)-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes.

• We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations.
• These symmetries can be labeled by an integer n.
• At each order n, the consistency relations constrain - completely for n=0,1, and partially for n>= 2 - the q^n behavior of the soft limits.