# The Weyl tensor correlator in cosmological spacetimes

## Abstract

We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ε and δ, and the result is shown to have the correct de Sitter limit as ε, δ → 0. Furthermore, it is seen that the Weyl tensor correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.

- Authors:

- Departament de Física Fonamental, Institut de Ciències del Cosmos (ICC), Universitat de Barcelona (UB), C/ Martí i Franquès 1, 08028 Barcelona (Spain)

- Publication Date:

- OSTI Identifier:
- 22382092

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2014; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CORRELATION FUNCTIONS; COSMOLOGICAL INFLATION; DE SITTER GROUP; DE SITTER SPACE; DEGREES OF FREEDOM; INFRARED DIVERGENCES; METRICS; PERTURBATION THEORY; PHASE SPACE; SCALAR FIELDS; SPACE-TIME; SPECTRA; TENSORS

### Citation Formats

```
Fröb, Markus B., E-mail: mfroeb@itp.uni-leipzig.de.
```*The Weyl tensor correlator in cosmological spacetimes*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/12/010.

```
Fröb, Markus B., E-mail: mfroeb@itp.uni-leipzig.de.
```*The Weyl tensor correlator in cosmological spacetimes*. United States. doi:10.1088/1475-7516/2014/12/010.

```
Fröb, Markus B., E-mail: mfroeb@itp.uni-leipzig.de. Mon .
"The Weyl tensor correlator in cosmological spacetimes". United States. doi:10.1088/1475-7516/2014/12/010.
```

```
@article{osti_22382092,
```

title = {The Weyl tensor correlator in cosmological spacetimes},

author = {Fröb, Markus B., E-mail: mfroeb@itp.uni-leipzig.de},

abstractNote = {We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ε and δ, and the result is shown to have the correct de Sitter limit as ε, δ → 0. Furthermore, it is seen that the Weyl tensor correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.},

doi = {10.1088/1475-7516/2014/12/010},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 12,

volume = 2014,

place = {United States},

year = {2014},

month = {12}

}