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.
