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 favour of the model where the modular part of the complex field plays the role of the inflaton whereas the argument part is the quintessence field. Numerical calculation shows that a heteroclinic orbit (solution of the dynamical system) is interpolated between early-time de Sitter phase (an unstable critical point) and a late-time de Sitter attractor.