Natural Quintessence and the Brane World
  Although quintessence models have attractive cosmological features, they face two major difficulties. First, it has not yet been possible to find one which convincingly realizes the goal of explaining present-day cosmic acceleration generically using only attractor solutions. Second, quintessence has proven difficult to obtain within realistic microscopic theories, largely due to two major obstructions. Both of these difficulties are summarized in this article, together with a recent proposal for circumventing the second of them within a brane-world context. It is shown that this proposal leads to a broader class of dynamics for the quintessence field, in which its couplings slowly run (or: walk) over cosmological time scales. The walking of the quintessence couplings opens up new possibilities for solving the first problem: that of obtaining acceptable transitions between attractor solutions. 
C.P. Burgess