Quintessence, cosmological horizons, and self-tuning

We point out that quintessence with an exponential potential V_0 exp(- betaphi / 3^{1/2} M_p) can account for the present observed acceleration of theuniverse, without necessarily leading to eternal acceleration. This occurs for2.4 < beta < 2.8. Thus a cosmological horizon, which is supposed to beproblematic within the context of string theory, can be avoided. We argue thatthis class of models is not particularly fine-tuned. We further examine thisquestion in the context of a modified Friedmann equation, H^2 ~ rho + p, whichis suggested by higher dimensional self-tuning approaches to the cosmologicalconstant problem. It is shown that the self-tuning case can also be consistentwith observations, if 1.8 < beta < 2.4. Future observations of high-zsupernovae will be able to test whether beta lies in the desired range.Comment: 13 pp., 5 figures; references adde