Supergravity inflation on a brane.

We discuss supergravity inflation in braneworld cosmology for the class of potentials $V(\phi)=\alpha \phi^n\rm{exp}(-\beta^m \phi^m)$ with $m=1,~2$. These minimal SUGRA models evade the $\eta$ problem due to a broken shift symmetry and can easily accommodate the observational constraints. Models with smaller $n$ are preferred while models with larger $n$ are out of the $2\sigma$ region. Remarkably, the field excursions required for $60$ $e$-foldings stay sub-planckian $\Delta\phi <1$.