  The isotropy and homogeneity of the cosmic microwave background (CMB) favors
"scalar driven" early Universe inflationary models. Non-scalar fields, and in
particular gauge fields, are on the other hand commonplace in all high energy
particle physics models proposed to be at work at the upper bound on energy
scale of inflation set by the current CMB observations. In this review we
consider the role and consequences, theoretical and observational, that gauge
fields can have during inflationary era. Gauge fields may be turned on in the
background during inflation, or may become relevant at the level of cosmic
perturbations. There have been two main class of models with gauge fields in
the background, models which show violation of cosmic no-hair theorem and those
which lead to isotropic FLRW cosmology, respecting the cosmic no-hair theorem.
Models in which gauge fields are only turned on at the cosmic perturbation
level, may source primordial magnetic fields. We also review specific
observational features of these models on the CMB and/or the primordial cosmic
magnetic fields. Our discussions will be mainly focused on the inflation
period, with only a brief discussion on the post inflationary (p)reheating era.
