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 \geq 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 \geq 2 are new .
As a check , we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation .