Inflationary scenarios from branes at angles

We describe a simple mechanism that can lead to 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: by slight relative rotations of the branes with small angles, by considering small relative velocities between the branes, by introducing orientifolds, etc. 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 anisotropies in the microwave background. Inflation ends as in hybrid inflation, triggered by the negative curvature of the string tachyon potential. In this paper we elaborate on one of the simplest examples: two almost parallel D4-branes in a flat compactified space.