Non-minimal coupling, exponential potentials and the $w<-1$ regime of dark energy

Recent observations and theoretical considerations have motivated the study of models for dark energy with equation of state characterized by a parameter $w=p/\rho<-1$. Such models, however, are usually believed to be inviable due to their instabilities against classical perturbations or potentially catastrophic vacuum decays. In this paper, we show that a simple quintessential model with potential $V(\phi)=Ae^{-\sigma\phi}$ and a gravitational coupling of the form $(1+|\xi|\phi^2)R$ can exhibit, for large sets of initial conditions, asymptotic de Sitter behavior with $w<-1$ regimes. Nevertheless, the model is indeed stable at classical and quantum level.