  Low energy supersymmetric models provide a solution to the hierarchy problem
and also have the necessary ingredients to solve two of the most outstanding
issues in cosmology: the origin of dark matter and baryonic matter. One of the
most attractive features of this framework is that the relevant physical
processes are related to interactions at the weak scale and therefore may be
tested in collider experiments in the near future. This is true for the Minimal
Supersymmetric Standard Model (MSSM) as well as for its extension with the
addition of one singlet chiral superfield, the so-called nMSSM. It has been
recently shown that within the nMSSM an elegant solution to both the problem of
baryogenesis and dark matter may be found, that relies mostly on the mixing of
the singlet sector with the Higgs sector of the theory. In this work we review
the nMSSM model constraints from cosmology and present the associated collider
phenomenology at the LHC and the ILC. We show that the ILC will efficiently
probe the neutralino, chargino and Higgs sectors, allowing to confront
cosmological observations with computations based on collider measurements. We
also investigate the prospects for a direct detection of dark matter and the
constraints imposed by the current bounds of the electron electric dipole
moment in this model.
