A cosmological model with complex scalar field
  In this paper, we wish to point out the possibility of using a complex scalar field to account for the inflationary stage and the current acceleration. By the analysis of the dynamical system and numerical work, we show that the amplitude of the complex scalar field plays the role of the inflaton whereas the phase is the quintessence field. The numerical solutions describe heteroclinic orbits, which interpolate between an unstable critical point and a late-time de Sitter attractor. Therefore, this model is more natural to explain the two stages of acceleration. 
Xiang-hua Zhai and Yi-bin Zhao