  We describe a detailed analytic model for predicting statistical quantities
(such as number counts, redshift distributions and sizes) of clusters detected
in blank-field, thermal Sunyaev-Zel'dovich effect experiments. We include in
this model the possibility of non-Gaussian density perturbations in the early
Universe and also describe a simple model for the effects of preheating on
cluster Sunyaev-Zel'dovich effect fluxes. We use this model to explore the
current state of the theoretical uncertainties present in this type of analytic
modelling, highlighting where further improvement will be necessary to fully
exploit forthcoming surveys. We then go on to explore the constraints on
cosmological parameters, the presence of any non-Gaussianity and the degree of
cluster preheating which may be obtained from both the BOLOCAM and PLANCK
experiments. We find that, providing redshifts can be measured for all detected
clusters, the BOLOCAM experiment may provide detections of non-Gaussianity or
preheating and could give approximate measurements of these effects if prior
knowledge of the various cosmological parameters is taken into account. The
PLANCK experiment Sunyaev-Zel'dovich effect cluster survey is predicted to
provide highly accurate (~5%) measurements of the degree of non-Gaussianity and
preheating while also providing measurements of several cosmological parameters
to accuracies of a few percent independent from those constraints that will be
derived from its detections of primordial cosmic microwave background
anisotropies.

Astrophysics