# Gravitational waves in viable f(R) models

## Abstract

We study gravitational waves in viable f(R) theories under a non-zero background curvature. In general, an f(R) theory contains an extra scalar degree of freedom corresponding to a massive scalar mode of gravitational wave. For viable f(R) models, since there always exits a de-Sitter point where the background curvature in vacuum is non-zero, the mass squared of the scalar mode of gravitational wave is about the de-Sitter point curvature R{sub d} ∼ 10{sup −66}eV{sup 2}. We illustrate our results in two types of viable f(R) models: the exponential gravity and Starobinsky models. In both cases, the mass will be in the order of 10{sup −33}eV when it propagates in vacuum. However, in the presence of matter density in galaxy, the scalar mode can be heavy. Explicitly, in the exponential gravity model, the mass becomes almost infinity, implying the disappearance of the scalar mode of gravitational wave, while the Starobinsky model gives the lowest mass around 10{sup −24}eV, corresponding to the lowest frequency of 10{sup −9} Hz, which may be detected by the current and future gravitational wave probes, such as LISA and ASTROD-GW.

- Authors:

- Department of Physics, National Tsing Hua University, Hsinchu 300, Taiwan (China)

- Publication Date:

- OSTI Identifier:
- 22277815

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2011; Journal Issue: 08; 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; ASTROPHYSICS; COSMOLOGICAL MODELS; COSMOLOGY; DE SITTER GROUP; DE SITTER SPACE; DEGREES OF FREEDOM; DENSITY; GALAXIES; GRAVITATIONAL WAVES; MASS; PROBES; SCALARS

### Citation Formats

```
Yang, Louis, Lee, Chung-Chi, and Geng, Chao-Qiang, E-mail: louis.lineage@msa.hinet.net, E-mail: geng@phys.nthu.edu.tw, E-mail: g9522545@oz.nthu.edu.tw.
```*Gravitational waves in viable f(R) models*. United States: N. p., 2011.
Web. doi:10.1088/1475-7516/2011/08/029.

```
Yang, Louis, Lee, Chung-Chi, & Geng, Chao-Qiang, E-mail: louis.lineage@msa.hinet.net, E-mail: geng@phys.nthu.edu.tw, E-mail: g9522545@oz.nthu.edu.tw.
```*Gravitational waves in viable f(R) models*. United States. doi:10.1088/1475-7516/2011/08/029.

```
Yang, Louis, Lee, Chung-Chi, and Geng, Chao-Qiang, E-mail: louis.lineage@msa.hinet.net, E-mail: geng@phys.nthu.edu.tw, E-mail: g9522545@oz.nthu.edu.tw. Mon .
"Gravitational waves in viable f(R) models". United States. doi:10.1088/1475-7516/2011/08/029.
```

```
@article{osti_22277815,
```

title = {Gravitational waves in viable f(R) models},

author = {Yang, Louis and Lee, Chung-Chi and Geng, Chao-Qiang, E-mail: louis.lineage@msa.hinet.net, E-mail: geng@phys.nthu.edu.tw, E-mail: g9522545@oz.nthu.edu.tw},

abstractNote = {We study gravitational waves in viable f(R) theories under a non-zero background curvature. In general, an f(R) theory contains an extra scalar degree of freedom corresponding to a massive scalar mode of gravitational wave. For viable f(R) models, since there always exits a de-Sitter point where the background curvature in vacuum is non-zero, the mass squared of the scalar mode of gravitational wave is about the de-Sitter point curvature R{sub d} ∼ 10{sup −66}eV{sup 2}. We illustrate our results in two types of viable f(R) models: the exponential gravity and Starobinsky models. In both cases, the mass will be in the order of 10{sup −33}eV when it propagates in vacuum. However, in the presence of matter density in galaxy, the scalar mode can be heavy. Explicitly, in the exponential gravity model, the mass becomes almost infinity, implying the disappearance of the scalar mode of gravitational wave, while the Starobinsky model gives the lowest mass around 10{sup −24}eV, corresponding to the lowest frequency of 10{sup −9} Hz, which may be detected by the current and future gravitational wave probes, such as LISA and ASTROD-GW.},

doi = {10.1088/1475-7516/2011/08/029},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 08,

volume = 2011,

place = {United States},

year = {2011},

month = {8}

}