On classical de Sitter and Minkowski solutions with intersecting branes

Motivated by the connection of string theory to cosmology or particle physics, we study solutions of type II supergravities having a four-dimensional de Sitter or Minkowski space-time, with intersecting Dp-branes and orientifold O-p-planes. Only few such solutions are known, and we aim at a better characterisation. Modulo a few restrictions, we prove that there exists no classical de Sitter solution for any combination of D-3/O-3 and D-7/O-7, while we derive interesting constraints for intersecting D-5/O-5 or D-6/O-6, or combinations of D-4/O-4 and D-8/O-8. Concerning classical Minkowski solutions, we understand some typical features, and propose a solution ansatz. Overall, a central information appears to be the way intersecting D-p/O-p overlap each other, a point we focus on.