Non-universal gaugino phases and the LSP relic density

The cosmological relic density of the lightest supersymmetric particle (LSP) of type I string derived model is calculated. This model can accommodate large values of CP violating phases, and the electron and neutron electric dipole moments satisfy the experimental constraint. We show that the constraint from the electric dipole moment on the ratio between the gaugino masses implies that the mass of the LSP, which is bino like, is close to the lightest chargino. The co-annihilation between them is very important to reduce the LSP relic density to an interesting region. We show that the SUSY phases, although they are large, have no significant effect on the relic density and on the the upper bound imposed on the LSP mass. However, they are very significant for the detection rates. We emphasize that the phase of the trilinear coupling increase the direct and indirect detection rates.