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(phi) = mu (alpha +4)phi (-alpha)], we show that in the quadratic dominant stage the density parameter of a scalar field Omega (phi) decreases as a(-4(alpha -2)/(alpha +2)) for 2<<alpha><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 <rho>(2)-dominant stage. Assuming an equipartition condition, we discuss constraints on parameters, with the result that alpha greater than or equal to4 is required. This constraint also restricts the value of the five-dimensional Planck mass, e.g., 4x10(-14)m(4)less than or similar tom(5)less than or similar to 3x10(-13)m(4) for alpha =5. For an exponential potential model V =mu (4) exp(-lambda phi /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 rho (2)-dominant stage, rather than the Omega (phi)-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 rho (2)-dominant stage, which provides a wider initial condition for successful quintessence.