### Abstract

We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass m^{2} = -2(2ℓ-1)(ℓ+1)H^{2} and m^{2} = -2ℓ(2ℓ+3)H ^{2} where ℓ is an integer. There are two branches (± branches) of solutions for the background spacetime. In the + branch, which includes the self-accelerating universe, a resonance appears for a mode with m^{2} = 2H^{2} due to a spin-0 perturbation with m^{2} = 2H^{2}. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with m^{2} = 2H^{2}. In the - branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of the van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the linearized gravity on the brane is well described by the Brans-Dicke theory with ω = 3Hr_{c} in the - branch and ω = -3Hr_{c} in the + branch, respectively, which confirms the existence of the ghost in the + branch. We also study large scale perturbations. In the + branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of the Weyl tensor in the bulk, but no instability is shown to exist on the brane.

Original language | English |
---|---|

Article number | 013 |

Journal | Journal of Cosmology and Astroparticle Physics |

Issue number | 7 |

DOIs | |

Publication status | Published - 2006 Jul 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cosmological perturbation theory
- Cosmology with extra dimensions
- Inflation

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of Cosmology and Astroparticle Physics*, (7), [013]. https://doi.org/10.1088/1475-7516/2006/07/013

**Inflaton perturbations in brane-world cosmology with induced gravity.** / Koyama, Kazuya; Mizuno, Shuntaro.

Research output: Contribution to journal › Article

*Journal of Cosmology and Astroparticle Physics*, no. 7, 013. https://doi.org/10.1088/1475-7516/2006/07/013

}

TY - JOUR

T1 - Inflaton perturbations in brane-world cosmology with induced gravity

AU - Koyama, Kazuya

AU - Mizuno, Shuntaro

PY - 2006/7/1

Y1 - 2006/7/1

N2 - We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass m2 = -2(2ℓ-1)(ℓ+1)H2 and m2 = -2ℓ(2ℓ+3)H 2 where ℓ is an integer. There are two branches (± branches) of solutions for the background spacetime. In the + branch, which includes the self-accelerating universe, a resonance appears for a mode with m2 = 2H2 due to a spin-0 perturbation with m2 = 2H2. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with m2 = 2H2. In the - branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of the van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the linearized gravity on the brane is well described by the Brans-Dicke theory with ω = 3Hrc in the - branch and ω = -3Hrc in the + branch, respectively, which confirms the existence of the ghost in the + branch. We also study large scale perturbations. In the + branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of the Weyl tensor in the bulk, but no instability is shown to exist on the brane.

AB - We study cosmological perturbations in the brane models with an induced Einstein-Hilbert term on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensional Minkowski spacetime. Inflaton fluctuations excite Kaluza-Klein modes of bulk metric perturbations with mass m2 = -2(2ℓ-1)(ℓ+1)H2 and m2 = -2ℓ(2ℓ+3)H 2 where ℓ is an integer. There are two branches (± branches) of solutions for the background spacetime. In the + branch, which includes the self-accelerating universe, a resonance appears for a mode with m2 = 2H2 due to a spin-0 perturbation with m2 = 2H2. The self-accelerating universe has a distinct feature because there is also a helicity-0 mode of spin-2 perturbations with m2 = 2H2. In the - branch, which can be thought as the Randall-Sundrum type brane-world with the high energy quantum corrections, there is no resonance. At high energies, we analytically confirm that four-dimensional Einstein gravity is recovered, which is related to the disappearance of the van Dam-Veltman-Zakharov discontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that the linearized gravity on the brane is well described by the Brans-Dicke theory with ω = 3Hrc in the - branch and ω = -3Hrc in the + branch, respectively, which confirms the existence of the ghost in the + branch. We also study large scale perturbations. In the + branch, the resonance induces a non-trivial anisotropic stress on the brane via the projection of the Weyl tensor in the bulk, but no instability is shown to exist on the brane.

KW - Cosmological perturbation theory

KW - Cosmology with extra dimensions

KW - Inflation

UR - http://www.scopus.com/inward/record.url?scp=42749108311&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42749108311&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2006/07/013

DO - 10.1088/1475-7516/2006/07/013

M3 - Article

AN - SCOPUS:42749108311

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

SN - 1475-7516

IS - 7

M1 - 013

ER -