# Tensor perturbations in a general class of Palatini theories

## Abstract

We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.

- Authors:

- Centre for Cosmology, Particle Physics and Phenomenology, Institute of Mathematics and Physics, Louvain University, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve (Belgium)
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm (Sweden)
- Depto. de Física Teórica and IFIC, Universidad de Valencia - CSIC, Calle Dr. Moliner 50, Burjassot 46100, Valencia (Spain)

- Publication Date:

- OSTI Identifier:
- 22525772

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 06; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; COSMOLOGICAL MODELS; COSMOLOGY; DISTURBANCES; GRAVITATION; IDEAL FLOW; MATHEMATICAL SOLUTIONS; METRICS; SPACE-TIME; STRESSES; TENSORS; TORSION

### Citation Formats

```
Jiménez, Jose Beltrán, Heisenberg, Lavinia, and Olmo, Gonzalo J., E-mail: jose.beltran@cpt.univ-mrs.fr, E-mail: laviniah@kth.se, E-mail: gonzalo.olmo@csic.es.
```*Tensor perturbations in a general class of Palatini theories*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/06/026.

```
Jiménez, Jose Beltrán, Heisenberg, Lavinia, & Olmo, Gonzalo J., E-mail: jose.beltran@cpt.univ-mrs.fr, E-mail: laviniah@kth.se, E-mail: gonzalo.olmo@csic.es.
```*Tensor perturbations in a general class of Palatini theories*. United States. doi:10.1088/1475-7516/2015/06/026.

```
Jiménez, Jose Beltrán, Heisenberg, Lavinia, and Olmo, Gonzalo J., E-mail: jose.beltran@cpt.univ-mrs.fr, E-mail: laviniah@kth.se, E-mail: gonzalo.olmo@csic.es. Mon .
"Tensor perturbations in a general class of Palatini theories". United States.
doi:10.1088/1475-7516/2015/06/026.
```

```
@article{osti_22525772,
```

title = {Tensor perturbations in a general class of Palatini theories},

author = {Jiménez, Jose Beltrán and Heisenberg, Lavinia and Olmo, Gonzalo J., E-mail: jose.beltran@cpt.univ-mrs.fr, E-mail: laviniah@kth.se, E-mail: gonzalo.olmo@csic.es},

abstractNote = {We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.},

doi = {10.1088/1475-7516/2015/06/026},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 06,

volume = 2015,

place = {United States},

year = {Mon Jun 01 00:00:00 EDT 2015},

month = {Mon Jun 01 00:00:00 EDT 2015}

}