  We explore a new class of supersymmetric models of inflation where the
inflaton is realised as a combination of a Higgs field and (gauge non-singlet)
matter fields, using a "tribrid" structure of the superpotential. Inflation is
associated with a phase transition around GUT scale energies. The inflationary
trajectory already preselects the later vacuum after inflation, which has the
advantage of automatically avoiding the production of dangerous topological
defects at the end of inflation. While at first sight the models look similar
to smooth inflation, they feature a waterfall and are therefore only
pseudosmooth. The new class of models offers novel possibilities for realising
inflation in close contact with particle physics, for instance with
supersymmetric GUTs or with supersymmetric flavour models based on family
symmetries.
