Slow-roll trajectories in Chromo-Natural and Gauge-flation Models, an exhaustive analysis

Inflation paradigm is the main framework for the earlyuniverse cosmology today which solves the old cosmo-logical puzzles such as horizon and flatness problems aswell as providing a natural mechanism for generating cos-mic perturbations. Despite of its many phenomenologicalsuccesses, however, inflation faces some theoretical chal-lenges. Most of the successful inflationary models in theliterature are based on using one or more scalar fieldswith a sufficiently flat potential to guarantee the slow-roll condition and leads to enough number of e-foldings.On the other hand, without providing a consistent highenergy theory setting, such extremely flat potentials gen-erally is not protected against the quantum correctionsunless we highly fine-tuned the system. This theoreticalconcern, the so-called η-problem, has driven many effortsto avoid fine-tuning in the potential. First used in Nat-ural Inflation [1, 2], one possible solution is consideringaxion fields as inflaton. In fact, since the axion field has aperturbatively exact cosine-type potential, it would notreceived any perturbative quantum corrections. How-ever, in order to have a successful slow-roll inflation, theaxion decay constant f should be very large in this model(f∼ M