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 () =^+4^-, we show that in the quadratic dominant stage the density parameter of a scalar field _ decreases as a^-4 (-2) / (+2) for 2~4 is required. This constraint also restricts the value of the five-dimensional Planck mass, e. g. , 410^-14m₄m₅310^-13m₄ for =5. For an exponential potential model V=^4exp (-/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 ^2-dominant stage, rather than the _-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 ^2-dominant stage, which provides a wider initial condition for successful quintessence.