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(Q) = μα+4Q-α (α≥2), we find that the density parameter of the scalar field decreases as ΩQ∼a-4(α-2)/(α+2) in the epoch of quadratic energy density dominance, if α≤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 α≳4.
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