Inflationary models with a flat potential enforced by non-abelian discrete gauge symmetries

Non-abelian discrete gauge symmetries can provide the inflaton with a flat potential even when one takes into account gravitational strength effects. The discreteness of the symmetries also provide special field values where inflation can end via a hybrid type mechanism. An interesting feature of this method is that it can naturally lead to extremely flat potentials and so, in principle, to inflation at unusually low energy scales. Two examples of effective field theories with this mechanism are given, one with a hybrid exit and one with a mutated hybrid exit. They include an explicit example in which the single field consistency condition is violated.