An infinite set of Ward identities for adiabatic modes in cosmology

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. The identities at n = 0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n = 1 gives the recently-discovered conformal consistency relations, and the identities for n ⩾ 2 are new. As a check, we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation.