### Abstract

We reanalyze a new quintessence scenario in a brane world model, assuming that a quintessence scalar field is confined in our three-dimensional brane world. We study three typical quintessence models: (1) an inverse-power-law potential, (2) an exponential potential, and (3) a kinetic-term quintessence (k-essence) model. With an inverse-power-law potential model [V(φ) = μ^{α+4}φ^{-α}], we show that in the quadratic dominant stage the density parameter of a scalar field Ω_{φ} decreases as a^{-4(α-2)/(α+2)} for 2<α<6, which is followed by the conventional quintessence scenario. This feature provides us wider initial conditions for successful quintessence. In fact, even if the universe is initially scalar-field dominated, it eventually evolves into a radiation dominated era in the ρ^{2}-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, with the result that α≥4 is required. This constraint also restricts the value of the five-dimensional Planck mass, e.g., 4×10^{-14}m_{4}≤m_{5}≤3×10 ^{-13}m_{4} for α=5. For an exponential potential model V = μ^{4} exp(-λφ/m_{4}), we may not find a natural and successful quintessence scenario as it is, while for a kinetic-term quintessence, we find a tracking solution even in the ρ^{2}-dominant stage, rather than the Ω_{φ}-decreasing solution for an inverse-power-law potential. Then we do find a slight advantage in a brane world. Only the density parameter increases more slowly in the ρ^{2}-dominant stage, which provides a wider initial condition for successful quintessence.

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

Article number | 123521 |

Journal | Physical Review D |

Volume | 64 |

Issue number | 12 |

Publication status | Published - 2001 Dec 15 |

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### ASJC Scopus subject areas

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

### Cite this

**Quintessence in a brane world.** / Mizuno, Shuntaro; Maeda, Keiichi.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 64, no. 12, 123521.

}

TY - JOUR

T1 - Quintessence in a brane world

AU - Mizuno, Shuntaro

AU - Maeda, Keiichi

PY - 2001/12/15

Y1 - 2001/12/15

N2 - We reanalyze a new quintessence scenario in a brane world model, assuming that a quintessence scalar field is confined in our three-dimensional brane world. We study three typical quintessence models: (1) an inverse-power-law potential, (2) an exponential potential, and (3) a kinetic-term quintessence (k-essence) model. With an inverse-power-law potential model [V(φ) = μα+4φ-α], we show that in the quadratic dominant stage the density parameter of a scalar field Ωφ decreases as a-4(α-2)/(α+2) for 2<α<6, which is followed by the conventional quintessence scenario. This feature provides us wider initial conditions for successful quintessence. In fact, even if the universe is initially scalar-field dominated, it eventually evolves into a radiation dominated era in the ρ2-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, with the result that α≥4 is required. This constraint also restricts the value of the five-dimensional Planck mass, e.g., 4×10-14m4≤m5≤3×10 -13m4 for α=5. For an exponential potential model V = μ4 exp(-λφ/m4), we may not find a natural and successful quintessence scenario as it is, while for a kinetic-term quintessence, we find a tracking solution even in the ρ2-dominant stage, rather than the Ωφ-decreasing solution for an inverse-power-law potential. Then we do find a slight advantage in a brane world. Only the density parameter increases more slowly in the ρ2-dominant stage, which provides a wider initial condition for successful quintessence.

AB - We reanalyze a new quintessence scenario in a brane world model, assuming that a quintessence scalar field is confined in our three-dimensional brane world. We study three typical quintessence models: (1) an inverse-power-law potential, (2) an exponential potential, and (3) a kinetic-term quintessence (k-essence) model. With an inverse-power-law potential model [V(φ) = μα+4φ-α], we show that in the quadratic dominant stage the density parameter of a scalar field Ωφ decreases as a-4(α-2)/(α+2) for 2<α<6, which is followed by the conventional quintessence scenario. This feature provides us wider initial conditions for successful quintessence. In fact, even if the universe is initially scalar-field dominated, it eventually evolves into a radiation dominated era in the ρ2-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, with the result that α≥4 is required. This constraint also restricts the value of the five-dimensional Planck mass, e.g., 4×10-14m4≤m5≤3×10 -13m4 for α=5. For an exponential potential model V = μ4 exp(-λφ/m4), we may not find a natural and successful quintessence scenario as it is, while for a kinetic-term quintessence, we find a tracking solution even in the ρ2-dominant stage, rather than the Ωφ-decreasing solution for an inverse-power-law potential. Then we do find a slight advantage in a brane world. Only the density parameter increases more slowly in the ρ2-dominant stage, which provides a wider initial condition for successful quintessence.

UR - http://www.scopus.com/inward/record.url?scp=0035893869&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035893869&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035893869

VL - 64

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 12

M1 - 123521

ER -