Kurt Hinterbichler, Lam Hui, Justin Khoury
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.
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http://arxiv.org/abs/1304.5527
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