  In this lecture I will review the present status of inflation within
string-based brane-world scenarios. The idea is to start from a supersymmetric
configuration with two parallel static Dp-branes, and slightly break the
supersymmetry conditions to produce a very flat potential for the field that
parametrises the distance between the branes, i.e. the inflaton field. This
breaking can be achieved in various ways. I will describe one of the simplest
examples described in Ref. [1]: two almost parallel D4-branes in a flat
compactified space, with a small relative angle between the branes, softly
breaking supersymmetry. If the breaking parameter is sufficiently small, a
large number of e-folds can be produced within the D-brane, for small changes
of the configuration in the compactified directions. Such a process is local,
i.e. it does not depend very strongly on the compactification space nor on the
initial conditions. Moreover, the breaking induces a very small velocity and
acceleration, which ensures very small slow-roll parameters and thus an almost
scale invariant spectrum of metric fluctuations, responsible for the observed
temperature and polarization anisotropies in the microwave background. Another
prediction of the model is the small amplitude of the gravitational wave
spectrum, which may not be detectable in the near future. Inflation ends as in
hybrid inflation, triggered by the negative curvature of the string tachyon
potential.
