Cosmological Fine Tuning, Supersymmetry, and the Gauge Heirarchy Problem

We study the extent to which the cosmological fine-tuning problem - why the relic density of neutralino cold dark matter particles $\chi$ is similar to that of baryons - is related to the fine-tuning aspect of the gauge hierarchy problem - how one arranges that M_W << M_P without unnatural choices of MSSM parameters. Working in the minimal supergravity framework with universal soft supersymmetry-breaking parameters as inputs, we find that the hierarchical fine tuning is minimized for \Omega_{\chi} h^2 \sim 0.1. Conversely, imposing \Omega_{\chi} h^2 < 1 does not require small hierarchical fine tuning, but the exceptions to this rule are rather special, with parameters chosen such that m_{\chi}\sim M_Z/2 or M_h/2, or else m_{\chi} \simgt m_t. In the first two cases, neutralino annihilation receives a large contribution from a direct-channel pole, whereas in the third case it is enhanced by the large top Yukawa coupling.