  We study cosmology on a conical brane in the six-dimensional
Einstein-Maxwell-dilaton system, where the extra dimensions are compactified by
a magnetic flux. We systematically construct exact cosmological solutions using
the fact that the system is equivalently described by (6+n)-dimensional pure
Einstein-Maxwell theory via dimensional reduction. In particular, we find a
power-law inflationary solution for a general dilatonic coupling. When the
dilatonic coupling is given by that of Nishino-Sezgin chiral supergravity, this
reduces to the known solution which is not inflating. The power-law solution is
shown to be the late-time attractor. We also investigate cosmological tensor
perturbations in this model using the (6+n)-dimensional description. We obtain
the separable equation of motion and find that there always exist a zero mode,
while tachyonic modes are absent in the spectrum. The mass spectrum of
Kaluza-Klein modes is obtained numerically.
