Permutation on hybrid natural inflation

We analyze a model of hybrid natural inflation based on the smallest non-Abelian discrete group $S_3$. Leading invariant terms in the scalar potential have an accidental global symmetry that is spontaneously broken, providing a pseudo-Goldstone boson that is identified as the inflaton. The $S_3$ symmetry restricts both the form of the inflaton potential and the couplings of the inflaton field to the waterfall fields responsible for the end of inflation. We identify viable points in the model parameter space. Although the power in tensor modes is small in most of the parameter space of the model, we identify parameter choices that yield potentially observable values of $r$ without super-Planckian initial values of the inflaton field.

Figure 1

The Lyth bound is evaded if the inflaton slowly rolls from a steep point in the potential to near the minimum before the waterfall fields turn on.