# 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)
- (Germany)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22454505

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 12; Other Information: PUBLISHER-ID: JCAP12(2014)010; OAI: oai:repo.scoap3.org:5061; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CORRELATION FUNCTIONS; COSMOLOGICAL INFLATION; DE SITTER SPACE; DEGREES OF FREEDOM; INFRARED DIVERGENCES; METRICS; PERTURBATION THEORY; PHASE SPACE; QUANTUM FIELD THEORY; SCALAR FIELDS; SPACE-TIME; SPECTRA; WEYL UNIFIED THEORY

### Citation Formats

```
Fröb, Markus B., and Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103 Leipzig.
```*The Weyl tensor correlator in cosmological spacetimes*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/12/010.

```
Fröb, Markus B., & Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103 Leipzig.
```*The Weyl tensor correlator in cosmological spacetimes*. United States. doi:10.1088/1475-7516/2014/12/010.

```
Fröb, Markus B., and Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103 Leipzig. Fri .
"The Weyl tensor correlator in cosmological spacetimes". United States.
doi:10.1088/1475-7516/2014/12/010.
```

```
@article{osti_22454505,
```

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

author = {Fröb, Markus B. and Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103 Leipzig},

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},

number = 12,

volume = 2014,

place = {United States},

year = {Fri Dec 05 00:00:00 EST 2014},

month = {Fri Dec 05 00:00:00 EST 2014}

}