Conformal consistency relation for single-field inflation and its observation.
Abstract: We show how in any single-field model, primordial correlation functions of \zeta are endowed with an SO(4,1) symmetry, with dilations and special conformal transformations non-linearly realized by \zeta. This allows us to generalize the single-field consistency relations to capture not only the leading term in the squeezed limit---going as 1/q^3, where q is the small wavevector---but also the subleading one, going as 1/q^2. This term, for an (n+1)-point function, is fixed in terms of the variation of the n-point function under a special conformal transformation. In light of this, we consider whether the non-Gaussian scale-dependent halo bias can be used not only to observe the local form of non-Gaussianity but also to distinguish among different shapes through the constraints on the behavior of the primordial three-point function in the squeezed limit.