Direct gauge mediation of supersymmetry breaking with a strongly coupled hidden sector

We analyze many aspects of the Pentagon Model as an example of direct Gauge Mediated Supersymmetry Breaking with a strongly coupled hidden sector, and as an implementation of Cosmological Supersymmetry Breaking (CSB). A pseudo-Nambu-Goldstone particle in the Pentagon is identified as a potential dark matter candidate, and the implications of this are explored. This leads to an attractive mechanism for baryogenesis which connects it to the dark matter density, however the parameters do not work well for the Pentagon in its original CSB context. The Pentagon is successfully embedded into an anomaly-free Grand Unified Theory, which can solve the doublet-triplet splitting problem and is compatible with proton decay experiments. However, it is found that the CSB parameters for the Pentagon are also incompatible with perturbative gauge coupling unification. The problems found with the Pentagon have led to the Pyramid Scheme, which is noted as a viable successor to the Pentagon Model. The Pyramid appears so far to be a working candidate for a CSB implementation. The Pentagon itself may still work as a model of direct gauge mediation, but fails to be a compelling implementation of CSB.