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 $w=p\mathrm{/}\rho <-1$. 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 $V(\varphi )=A{e}^{-\sigma \varphi }$ and a gravitational coupling of the form $(1+\mathrm{\mid }\xi \mathrm{\mid }{\varphi }^2)R$ 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.