### Abstract

We apply the renormalization group (RG) method to examine the observable scaling properties in Newtonian cosmology. The original scaling properties of the equations of motion in our model are modified for averaged observables on constant time slices. In the RG flow diagram, we find three robust fixed points: Einstein-de Sitter, Milne, and quiescent fixed points. Their stability (or instability) property does not change under the effect of fluctuations. Inspired by the inflationary scenario in the early Universe, we set the Einstein-de Sitter fixed point with small fluctuations as the boundary condition at the horizon scale. Solving the RG equations under this boundary condition toward the smaller scales, we find a generic behavior of observables such that the density parameter Ω decreases, while the Hubble parameter H increases for a smaller averaging volume. The quantitative scaling properties are analyzed by calculating the characteristic exponents around each fixed point. Finally we argue the possible fractal structure of the Universe beyond the horizon scale.

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

Article number | 043502 |

Pages (from-to) | 435021-4350218 |

Number of pages | 3915198 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 58 |

Issue number | 4 |

Publication status | Published - 1998 Aug 15 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*58*(4), 435021-4350218. [043502].

**Renormalization group approach in Newtonian cosmology.** / Sota, Yasuhide; Kobayashi, Toshiyuki; Maeda, Keiichi; Kurokawa, Tomomi; Morikawa, Masahiro; Nakamichi, Akika.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 58, no. 4, 043502, pp. 435021-4350218.

}

TY - JOUR

T1 - Renormalization group approach in Newtonian cosmology

AU - Sota, Yasuhide

AU - Kobayashi, Toshiyuki

AU - Maeda, Keiichi

AU - Kurokawa, Tomomi

AU - Morikawa, Masahiro

AU - Nakamichi, Akika

PY - 1998/8/15

Y1 - 1998/8/15

N2 - We apply the renormalization group (RG) method to examine the observable scaling properties in Newtonian cosmology. The original scaling properties of the equations of motion in our model are modified for averaged observables on constant time slices. In the RG flow diagram, we find three robust fixed points: Einstein-de Sitter, Milne, and quiescent fixed points. Their stability (or instability) property does not change under the effect of fluctuations. Inspired by the inflationary scenario in the early Universe, we set the Einstein-de Sitter fixed point with small fluctuations as the boundary condition at the horizon scale. Solving the RG equations under this boundary condition toward the smaller scales, we find a generic behavior of observables such that the density parameter Ω decreases, while the Hubble parameter H increases for a smaller averaging volume. The quantitative scaling properties are analyzed by calculating the characteristic exponents around each fixed point. Finally we argue the possible fractal structure of the Universe beyond the horizon scale.

AB - We apply the renormalization group (RG) method to examine the observable scaling properties in Newtonian cosmology. The original scaling properties of the equations of motion in our model are modified for averaged observables on constant time slices. In the RG flow diagram, we find three robust fixed points: Einstein-de Sitter, Milne, and quiescent fixed points. Their stability (or instability) property does not change under the effect of fluctuations. Inspired by the inflationary scenario in the early Universe, we set the Einstein-de Sitter fixed point with small fluctuations as the boundary condition at the horizon scale. Solving the RG equations under this boundary condition toward the smaller scales, we find a generic behavior of observables such that the density parameter Ω decreases, while the Hubble parameter H increases for a smaller averaging volume. The quantitative scaling properties are analyzed by calculating the characteristic exponents around each fixed point. Finally we argue the possible fractal structure of the Universe beyond the horizon scale.

UR - http://www.scopus.com/inward/record.url?scp=0542422647&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0542422647&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0542422647

VL - 58

SP - 435021

EP - 4350218

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 4

M1 - 043502

ER -