# General covariance constraints on cosmological correlators

## Abstract

We study the extent to which diffeomorphism invariance restricts the properties of the perturbations in single scalar field cosmological models. We derive a set of identities that constrain the connected correlators of the cosmological perturbations, as well as the one-particle-irreducible vertices of the theory in any gauge. These identities are the analogues of Slavnov-Taylor identities in gauge theories, and follow essentially from diffeomorphism invariance alone. Yet because quantization requires diffeomorphism invariance to be broken, they not only reflect invariance under diffeomorphisms, but also how the latter has been broken by gauge fixing terms. In order not to lose the symmetry altogether, we cannot simply set some fields to zero, as is usually done in cosmological perturbation theory, but need to decouple them smoothly and make sure that they do not contribute to cosmological correlators in the decoupling limit. We use these identities to derive a set of consistency relations between bispectra and power spectra of cosmological perturbations in different gauges. Without additional assumptions, these consistency relations just seem to reflect the redundancy implied by diffeomorphisms. But when combined with analyticity, in a formulation of the theory in which auxiliary fields have been integrated out, we recover novel and previously derivedmore »

- Authors:

- Department of Physics, Syracuse University, Syracuse, NY 13244-1130 (United States)
- Physics Department and Institute for Strings, Cosmology, and Astroparticle Physics, Columbia University, New York, NY 10027 (United States)

- Publication Date:

- OSTI Identifier:
- 22382013

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 01; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DECOUPLING; GAUGE INVARIANCE; LIMITING VALUES; PERTURBATION THEORY; QUANTIZATION; SCALAR FIELDS; SPECTRA; SYMMETRY

### Citation Formats

```
Armendariz-Picon, Cristian, Neelakanta, Jayanth T., and Penco, Riccardo, E-mail: carmenda@syr.edu, E-mail: jtneelak@syr.edu, E-mail: rpenco@columbia.edu.
```*General covariance constraints on cosmological correlators*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/01/035.

```
Armendariz-Picon, Cristian, Neelakanta, Jayanth T., & Penco, Riccardo, E-mail: carmenda@syr.edu, E-mail: jtneelak@syr.edu, E-mail: rpenco@columbia.edu.
```*General covariance constraints on cosmological correlators*. United States. doi:10.1088/1475-7516/2015/01/035.

```
Armendariz-Picon, Cristian, Neelakanta, Jayanth T., and Penco, Riccardo, E-mail: carmenda@syr.edu, E-mail: jtneelak@syr.edu, E-mail: rpenco@columbia.edu. Thu .
"General covariance constraints on cosmological correlators". United States.
doi:10.1088/1475-7516/2015/01/035.
```

```
@article{osti_22382013,
```

title = {General covariance constraints on cosmological correlators},

author = {Armendariz-Picon, Cristian and Neelakanta, Jayanth T. and Penco, Riccardo, E-mail: carmenda@syr.edu, E-mail: jtneelak@syr.edu, E-mail: rpenco@columbia.edu},

abstractNote = {We study the extent to which diffeomorphism invariance restricts the properties of the perturbations in single scalar field cosmological models. We derive a set of identities that constrain the connected correlators of the cosmological perturbations, as well as the one-particle-irreducible vertices of the theory in any gauge. These identities are the analogues of Slavnov-Taylor identities in gauge theories, and follow essentially from diffeomorphism invariance alone. Yet because quantization requires diffeomorphism invariance to be broken, they not only reflect invariance under diffeomorphisms, but also how the latter has been broken by gauge fixing terms. In order not to lose the symmetry altogether, we cannot simply set some fields to zero, as is usually done in cosmological perturbation theory, but need to decouple them smoothly and make sure that they do not contribute to cosmological correlators in the decoupling limit. We use these identities to derive a set of consistency relations between bispectra and power spectra of cosmological perturbations in different gauges. Without additional assumptions, these consistency relations just seem to reflect the redundancy implied by diffeomorphisms. But when combined with analyticity, in a formulation of the theory in which auxiliary fields have been integrated out, we recover novel and previously derived relations that follow from invariance under both time and spatial diffeomorphisms.},

doi = {10.1088/1475-7516/2015/01/035},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 01,

volume = 2015,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}