  We consider, in the context of a braneworld cosmology, the motion of the
universe coupled to a four-form gauge field, with constant field strength,
defined in higher dimensions. It is found, under rather general initial
conditions, that in this situation there is a period of exponential inflation
combined with cyclotron motion in the inflaton field space. The main effect of
the cyclotron motion is that conditions on the flatness of the inflaton
potential, which are typically necessary for exponential inflation, can be
evaded. There are Landau levels associated with the four-form gauge field, and
these correspond to quantum excitations of the inflaton field.
