Brane quintessence

We propose a new quintessence scenario in brane cosmology, assuming that a quintessence field Q is confined in our three-dimensional brane world. With a potential $V\left(Q\right)={\mu }^{\alpha +4\mathrm{}}{Q}^{-\alpha }$ $(\alpha >~2),$ we find that the density parameter of the scalar field decreases as ${\Omega }_Q\sim a^{-4\left(\alpha -2\right)/(\alpha +2)}$ in the epoch of quadratic energy density dominance, if $\alpha <~6.$ This attractor solution is followed by the usual tracking quintessence scenario after a conventional Friedmann universe is recovered. With an equipartition of initial energy density, we find a natural and successful quintessence model for $\alpha \gtrsim 4.$