  Low energy supersymmetry is motivated by its use as a solution to the
hierarchy problem of the electroweak scale. Having motivated this model with
naturalness arguments, it is then necessary to check whether the experimentally
allowed parameter space permits realisations of the model with low fine tuning.
The scope of this thesis is a study of naturalness of the electroweak physics
in the minimal supergravity model. The latest experimental constraints are
applied, and the fine tuning is quantitatively evaluated for a scan across the
parameter space. The fine tuning of the electroweak scale is evaluated at
2-loop order, and the fine tuning of the neutralino dark matter thermal relic
energy density is also determined. The natural regions of the parameter space
are identified and the associated phenomenology relevant for detection
discussed. Naturalness limits are also found for the parameter space and
spectrum. The minimum fine tuning found is 1 part in 9 when dark matter
constraints are neglected, and 1 part in 15 when dark matter constraints are
satisfied. For both cases, the minimum fine tuning is found for a Higgs mass of
115 GeV irrespective of whether the Higgs mass constraint is applied or not.
The most natural spectrum includes light superpartner fermions, and heavy
superpartner scalars. Minimal supergravity currently remains viable with
respect to naturalness and a natural realisation may be discovered within the
next couple of years.
