A single-field consistency relation for the three-point function

Abstract

We point out the existence of a consistency relation involving the three-point function of scalar perturbations which is valid in any inflationary model, independently of the inflaton Lagrangian under the assumption that the inflaton is the only dynamical field. The three-point function in the limit in which one of the momenta is much smaller than the other two is fixed in terms of the power spectrum and its tilt. This relation, although very hard to verify experimentally, could be easily proved wrong by forthcoming data, thus ruling out any scenario with a single dynamical field in a model independent way.