Attractor solution of phantom field

Abstract

In light of a recent study on the dark energy models that manifest an equation of state $w<\ensuremath{-}1,$ we investigate the cosmological evolution of a phantom field in a specific potential, exponential potential in this paper. The phase plane analysis shows that the there is a late time attractor solution in this model, which addresses similar issues to that of fine-tuning problems in conventional quintessence models. The evolution of the state w is determined by the attractor solution which is dependent on the $\ensuremath{\lambda}$ parameter in the potential. We also show that this model is stable for our present observable universe.