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

## TL;DR

This paper explores generalized disformal transformations in the Effective Field Theory of Inflation, showing how they can simplify the action and constrain modifications to cosmological correlators, especially at leading order in derivatives.

## Contribution

It introduces a systematic way to use disformal transformations to reduce the number of independent operators in the EFT of Inflation, clarifying their impact on observable correlators.

## Key findings

- Six operators can be set to zero at cubic order using transformations.
- Tensor three-point functions are unaffected at leading order in derivatives.
- Scalar-tensor-tensor correlators can be modified by changing scalar dynamics.

## 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.