Fine Tuning in Quintessence Models with Exponential Potentials

Abstract

We explore regions of parameter space in a simple exponential model of the form $V = V_0 e^{- \lambda \frac{Q}{M_p}}$ 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 $\lambda$ has to be less than $\sqrt{3}$ and the fixed point $\Omega_Q = 1$ has not been reached. All values of the parameter $\lambda$ that lead to this transient regime are permitted. We also point out that this model can accelerate the universe today even for $\lambda > \sqrt{2}$, 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.