Fine Tuning in Quintessence Models with Exponential Potentials

We explore regions of parameter space in a simple exponential model of the form V = V0 e −λ Q Mp that are allowed by observational constraints. We find that the level of fine tuning in these models is not different from more sophisticated models of dark energy. We study a transient regime where the parameter λ has to be less than √ 3 and the fixed point ΩQ = 1 has not been reached. All values of the parameter λ that lead to this transient regime are permitted. We also point out that this model can accelerate the universe today even for λ > √ 2, leading to a halt of the present acceleration of the universe in the future thus avoiding the horizon problem. We conclude that this model can not be discarded by current observations.