### 抄録

The stability condition of (the four-dimensional Friedmann universe)*(a compact internal space) (F^{4}*K^{D}) is presented for a class of higher-dimensional theories, in which the effective potential depends only on a scale length of the internal space. The Candelas-Weinberg model (i.e. one-loop quantum correction+a cosmological constant Lambda ), eleven-dimensional supergravity+ Lambda , Einstein-Yang-Mills theory and six-dimensional Einstein-Maxwell theory are classified into this class. It is shown that the F^{4}*K^{D} solution is stable against small perturbations in the above models. The stability against non-linear perturbation is also investigated. The author finds that the stable F^{4}*K^{D} solution is an attractor for a finite range of initial conditions if the proper volume of the universe is increasing with time.

元の言語 | English |
---|---|

記事番号 | 017 |

ページ（範囲） | 233-247 |

ページ数 | 15 |

ジャーナル | Classical and Quantum Gravity |

巻 | 3 |

発行部数 | 2 |

DOI | |

出版物ステータス | Published - 1986 |

外部発表 | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### これを引用

*Classical and Quantum Gravity*,

*3*(2), 233-247. [017]. https://doi.org/10.1088/0264-9381/3/2/017

**Stability and attractor in a higher-dimensional cosmology. I.** / Maeda, Keiichi.

研究成果: Article

*Classical and Quantum Gravity*, 巻. 3, 番号 2, 017, pp. 233-247. https://doi.org/10.1088/0264-9381/3/2/017

}

TY - JOUR

T1 - Stability and attractor in a higher-dimensional cosmology. I

AU - Maeda, Keiichi

PY - 1986

Y1 - 1986

N2 - The stability condition of (the four-dimensional Friedmann universe)*(a compact internal space) (F4*KD) is presented for a class of higher-dimensional theories, in which the effective potential depends only on a scale length of the internal space. The Candelas-Weinberg model (i.e. one-loop quantum correction+a cosmological constant Lambda ), eleven-dimensional supergravity+ Lambda , Einstein-Yang-Mills theory and six-dimensional Einstein-Maxwell theory are classified into this class. It is shown that the F4*KD solution is stable against small perturbations in the above models. The stability against non-linear perturbation is also investigated. The author finds that the stable F4*KD solution is an attractor for a finite range of initial conditions if the proper volume of the universe is increasing with time.

AB - The stability condition of (the four-dimensional Friedmann universe)*(a compact internal space) (F4*KD) is presented for a class of higher-dimensional theories, in which the effective potential depends only on a scale length of the internal space. The Candelas-Weinberg model (i.e. one-loop quantum correction+a cosmological constant Lambda ), eleven-dimensional supergravity+ Lambda , Einstein-Yang-Mills theory and six-dimensional Einstein-Maxwell theory are classified into this class. It is shown that the F4*KD solution is stable against small perturbations in the above models. The stability against non-linear perturbation is also investigated. The author finds that the stable F4*KD solution is an attractor for a finite range of initial conditions if the proper volume of the universe is increasing with time.

UR - http://www.scopus.com/inward/record.url?scp=0001094842&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001094842&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/3/2/017

DO - 10.1088/0264-9381/3/2/017

M3 - Article

AN - SCOPUS:0001094842

VL - 3

SP - 233

EP - 247

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 2

M1 - 017

ER -