# Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings

## 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.

- Authors:

- SISSA, via Bonomea 265, 34136, Trieste (Italy)
- Physics Department and INFN, Università di Roma 'La Sapienza', P.le Aldo Moro 2, 00185, Rome (Italy)
- Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy)
- Institut de physique théorique, Université Paris Saclay, CEA, CNRS, 91191 Gif-sur-Yvette (France)

- Publication Date:

- OSTI Identifier:
- 22667668

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRECTIONS; DISTURBANCES; FIELD THEORIES; HILBERT TRANSFORMATION; INFLATIONARY UNIVERSE; INFLATONS; METRICS; PERTURBATION THEORY; SPECTRA; TRANSFORMATIONS

### Citation Formats

```
Bordin, Lorenzo, Cabass, Giovanni, Creminelli, Paolo, and Vernizzi, Filippo, E-mail: lbordin@sissa.it, E-mail: giovanni.cabass@roma1.infn.it, E-mail: creminel@ictp.it, E-mail: filippo.vernizzi@cea.fr.
```*Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/09/043.

```
Bordin, Lorenzo, Cabass, Giovanni, Creminelli, Paolo, & Vernizzi, Filippo, E-mail: lbordin@sissa.it, E-mail: giovanni.cabass@roma1.infn.it, E-mail: creminel@ictp.it, E-mail: filippo.vernizzi@cea.fr.
```*Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings*. United States. doi:10.1088/1475-7516/2017/09/043.

```
Bordin, Lorenzo, Cabass, Giovanni, Creminelli, Paolo, and Vernizzi, Filippo, E-mail: lbordin@sissa.it, E-mail: giovanni.cabass@roma1.infn.it, E-mail: creminel@ictp.it, E-mail: filippo.vernizzi@cea.fr. Fri .
"Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings". United States. doi:10.1088/1475-7516/2017/09/043.
```

```
@article{osti_22667668,
```

title = {Simplifying the EFT of Inflation: generalized disformal transformations and redundant couplings},

author = {Bordin, Lorenzo and Cabass, Giovanni and Creminelli, Paolo and Vernizzi, Filippo, E-mail: lbordin@sissa.it, E-mail: giovanni.cabass@roma1.infn.it, E-mail: creminel@ictp.it, E-mail: filippo.vernizzi@cea.fr},

abstractNote = {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.},

doi = {10.1088/1475-7516/2017/09/043},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 09,

volume = 2017,

place = {United States},

year = {2017},

month = {9}

}