Cosmological fine tuning, supersymmetry and the gauge hierarchy problem

We study the extent to which the cosmological fine-tuning problem – why the relic density of neutralino cold dark matter particles χ is similar to that of baryons – is related to the fine-tuning aspect of the gauge hierarchy problem – how one arranges that MW≪MP 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 Ωχh2∼0.1. Conversely, imposing Ωχh2<1 does not require small hierarchical fine tuning, but the exceptions to this rule are rather special, with parameters chosen such that mχ∼MZ/2 or Mh/2, or else mχ≳mt. 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.