A Simple Model for Quintessential Inflation

We describe a simple toy model for quintessential inflation where a complex scalar field described by a lagrangian with a Peccei-Quinn U(1) symmetry spontaneously broken at a high energy scale and explicitly broken by instanton effects at a much lower energy can account for both the early inflationary phase and the recent accelerated expansion of the Universe. The real part of the complex field plays the role of the inflaton whereas the imaginary part, the “axion”, is the quintessence field.