Relic Densities of Dark Matter in the U(1)-Extended NMSSM and the Gauged Axion Supermultiplet

We compute the dark matter relic densities of neutralinos and axions in a supersymmetric model with a gauged anomalous U(1) symmetry, kinetically mixed with $U(1)_Y$ of hypercharge. The model is a variant of the USSM (the U(1) extended NMSSM), containing an extra U(1) symmetry and an extra singlet in the superpotential respect to the MSSM, where gauge invariance is restored by Peccei-Quinn interactions using a Stuckelberg multiplet. This approach introduces an axion (Im b) and a saxion (Re b) in the spectrum and generates an axino component for the neutralino. The Stuckelberg axion (Im b) develops a physical component (the gauged axion) after electroweak symmetry breaking. We classify all the interactions of the Lagrangian and perform a complete simulation study of the spectrum, determining the neutralino relic densities using micrOMEGAs. We discuss the phenomenological implications of the model analyzing mass values for the axion from the milli-eV to the MeV region. The possible scenarios that we analyze are significantly constrained by a combination of WMAP data, the exclusion limits from direct axion searches and the veto on late entropy release at the time of nucleosynthesis.