Quintessence in a brane world

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+4φ^-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 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^-14m₄m₅3×10^-13m₄ for α=5. For an exponential potential model V=μ⁴exp(-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 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 ρ²-dominant stage, which provides a wider initial condition for successful quintessence.