  An extensive sample of galaxy clusters will be available in the coming years,
detected through their Sunyaev-Zeldovich effect (SZE). We use a semi-analytic
model to study the scientific yield of combining SZE data with X-ray and
optical follow-up observations. If clusters at a given redshift z_o can be
identified with virialized, spherical halos, they populate a well-defined
"fundamental plane" (FP) in the parameter space of the three observables:
virial temperature (T), total Sunyaev-Zeldovich flux decrement (DS), and
angular size (theta). The location and orientation of the FP, as well as its
redshift-evolution, are sensitive to both the internal evolution of clusters,
and to the underlying cosmological parameters. We show that if clusters are not
standard candles (e.g. due to feedback, or energy injection), then this can be
inferred from the FP. Likewise, we study the dependence of the FP on the
cosmological parameters h, sigma_8, and Omega_0, and quantify constraints on
these parameters. We also show that in the absence of any non-gravitational
effects, the scatter in the the (DS-T) plane is significantly smaller than in
either the (theta-T) or the (theta-DS) planes. As a result, the (DS-T) relation
can be an exceptionally sensitive probe of both cluster physics and
cosmological parameters, and a comparison of the amount of scatter in these
three scaling relations will serve as a test of the origin (cosmological vs.
stochastic) of the scatter.
