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.
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