  A spontaneously broken global discrete symmetry may have pseudo Goldstone
modes associated with the spontaneous breaking of the approximate continuous
symmetry of the low dimension terms in the Lagrangian. These provide natural
candidates for an inflaton that can generate slow roll inflation. We show that,
in the case of a non Abelian discrete symmetry, the pseudo Goldstone modes
readily couple to further scalar fields in a manner that the end of inflation
is determined by these additional scalar fields, generating hybrid inflation.
We give a simple parameterisation of the inflationary potential in this case,
determine the inflationary parameters resulting, and show that phenomenological
successful inflation is possible while keeping the scale of symmetry breaking
sub-Plankian. Unlike natural inflation the inflation scale can be very low. We
construct two simple hybrid inflation models, one non supersymmetric and one
supersymmetric. In the latter case no parameters need be chosen anomalously
small.
