Some Consequences of Dark Energy Density varying Exponentially with   Scale Factor
  In this paper we have explored the consequences of a model of dark energy with its energy density varying exponentially with the scale factor. We first consider the model with $ \rho_{\phi} \propto e^{\kappa a} $, where $\kappa $ is a constant. This is a kind of generalisation of the cosmological constant model with $\kappa = 0$. We show that such an exponentially varying dark energy density with the scale factor naturally leads to an equivalent phantom field. We also consider a model with $ \rho_{\phi} \propto e^{\kappa /a} $ and we show that this also naturally leads to an equivalent phantom field. 
Sanil Unnikrishnan, T. R. Seshadri