# Metric-affine formalism of higher derivative scalar fields in cosmology

## Abstract

Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many interests in the phenomenological studies of infrared modifications of gravity. These theories are mostly studied by the metric variational approach in which only the metric is the fundamental field to account for the gravitation. In this paper we study the higher derivative scalar fields with the metric-affine formalism where the affine connection is treated arbitrarily at the beginning. Because the higher derivative scalar fields couple to the connection directly in a covariant theory these two formalisms will lead to different results. These differences are suppressed by the powers of the Planck mass and are usually expected to have small effects. But in some cases they may cause non-negligible deviations. We show by a higher derivative dark energy model that the two formalisms lead to significantly different pictures of the future universe.

- Authors:

- Department of Physics, Nanjing University, Hankou Road 22, Nanjing 210093 (China)

- Publication Date:

- OSTI Identifier:
- 22279838

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2012; Journal Issue: 07; 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; ACCELERATION; ASTROPHYSICS; COSMOLOGY; GRAVITATION; MASS; METRICS; NONLUMINOUS MATTER; POTENTIALS; SCALAR FIELDS; UNIVERSE; VARIATIONAL METHODS

### Citation Formats

```
Li, Mingzhe, and Wang, Xiulian, E-mail: limz@nju.edu.cn, E-mail: wangxiulian2000@yahoo.com.cn.
```*Metric-affine formalism of higher derivative scalar fields in cosmology*. United States: N. p., 2012.
Web. doi:10.1088/1475-7516/2012/07/010.

```
Li, Mingzhe, & Wang, Xiulian, E-mail: limz@nju.edu.cn, E-mail: wangxiulian2000@yahoo.com.cn.
```*Metric-affine formalism of higher derivative scalar fields in cosmology*. United States. doi:10.1088/1475-7516/2012/07/010.

```
Li, Mingzhe, and Wang, Xiulian, E-mail: limz@nju.edu.cn, E-mail: wangxiulian2000@yahoo.com.cn. Sun .
"Metric-affine formalism of higher derivative scalar fields in cosmology". United States. doi:10.1088/1475-7516/2012/07/010.
```

```
@article{osti_22279838,
```

title = {Metric-affine formalism of higher derivative scalar fields in cosmology},

author = {Li, Mingzhe and Wang, Xiulian, E-mail: limz@nju.edu.cn, E-mail: wangxiulian2000@yahoo.com.cn},

abstractNote = {Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many interests in the phenomenological studies of infrared modifications of gravity. These theories are mostly studied by the metric variational approach in which only the metric is the fundamental field to account for the gravitation. In this paper we study the higher derivative scalar fields with the metric-affine formalism where the affine connection is treated arbitrarily at the beginning. Because the higher derivative scalar fields couple to the connection directly in a covariant theory these two formalisms will lead to different results. These differences are suppressed by the powers of the Planck mass and are usually expected to have small effects. But in some cases they may cause non-negligible deviations. We show by a higher derivative dark energy model that the two formalisms lead to significantly different pictures of the future universe.},

doi = {10.1088/1475-7516/2012/07/010},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 07,

volume = 2012,

place = {United States},

year = {2012},

month = {7}

}