Scalar fields generating contemporary inflation

The evidence for an accelerating expansion of our Universe at the present epoch have led us to look for an energy component which could generate it. That may consist in quintessence in the form of a system of scalar fields {φa} rolling down a potential V({φ a}). This master's thesis presents the equations relevant to the cosmological evolution of such a system, along with the different conditions required for a viable cosmology. Also, via the exploration of two distinct models, two fundamental problems of quintessence theory are outlined. The impossibility of escaping the fine-tuning of initial conditions is first presented in link to the Liouville's theorem, and second the difficulty of avoiding the coincidence of the recent rise of quintessence even in the presence of attractors is shown