BICEP2 possible observation of primordial gravitational waves have been extensively
discussed during the past few months since this would be a window to new physics at
the scale of 10^16 GeV; this observations could disfavor several well grounded
inflationary models, consequently a test of this models with BICEP2 results is of
interest. An introduction to inflation and the slow-roll approximation which is used
in most of the recent models will be presented; also an explanation of the fine
tuning problem in the slow roll approximation and the solution with Natural
Inflation. The problems that Natural Inflation faces when trying to accommodate
Planck and BICEP2 results will be shown. And finally a discussion on how the model
of Hybrid Natural Inflation could be a better alternative to fit BICEP2 observations
of gravitational waves and what happens at the maximum of the tensor index is
presented.