Dynamics of Quintessential Inflation
  In this paper, we study a realistic model of quintessential inflation with radiation and matter. By the analysis of the dynamical system and numerical work about the evolution of the equation of state and cosmic density parameter, we show that this model is a good match for the current astronomical observation. The conclusion we obtain is in favor of the model where the modular part of complex field plays the role of the inflaton whereas the argument part is the quintessence field. The numerical calculation shows that a heteroclinic orbit (solution of dynamical system) which interpolates between early-time de Sitter phase (an unstable critical point) and a late-time de Sitter attractor. 
Xiang-hua Zhai and Yi-bin Zhao