Simplifying the EFT of Inflation: Generalized Disformal Transformations and Redundant Couplings

TL;DR

The paper addresses the redundancy of operators in the EFT of Inflation by analyzing generalized disformal transformations that include metric derivatives. It shows that late-time observables are invariant under these transformations, while the operator basis can be significantly simplified: up to two derivatives and cubic order, six free functions can remove six of the seventeen operators, fixing tensor couplings and constraining the tensor and mixed correlators; at higher derivatives, a set of transformations leaving the Einstein–Hilbert action intact further reduces the inflaton sector. The authors identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum, and assess which tensor operators remain non-eliminable, potentially yielding observable signatures in $\langle \gamma\gamma\gamma\rangle$ and $\langle \gamma\gamma\zeta\rangle$. In the decoupling limit, they show that Goldstone-field redefinitions provide an extra layer of freedom not always captured by unitary-gauge transformations, clarifying the relationship between different presentations of the EFTI. Overall, the work furnishes a principled framework to isolate the physically relevant higher-derivative corrections and highlights opportunities for phenomenological probes of tensor modes and mixed correlators.

Abstract

We study generalized disformal transformations, including derivatives of the metric, in the context of the Effective Field Theory of Inflation. All these transformations do not change the late-time cosmological observables but change the coefficients of the operators in the action: some couplings are effectively redundant. At leading order in derivatives and up to cubic order in perturbations, one has 6 free functions that can be used to set to zero 6 of the 17 operators at this order. This is used to show that the tensor three-point function cannot be modified at leading order in derivatives, while the scalar-tensor-tensor correlator can only be modified by changing the scalar dynamics. At higher order in derivatives there are transformations that do not affect the Einstein-Hilbert action: one can find 6 additional transformations that can be used to simplify the inflaton action, at least when the dynamics is dominated by the lowest derivative terms. We also identify the leading higher-derivative corrections to the tensor power spectrum and bispectrum.