  We discuss how future cluster surveys can constrain cosmological parameters
with particular reference to the properties of the dark energy component
responsible for the observed acceleration of the universe by probing the
evolution of the surface density of clusters as a function of redshift. We
explain how the abundance of clusters selected using their Sunyaev-Zel'dovich
effect can be computed as a function of the observed flux and redshift taking
into account observational effects due to a finite beam-size. By constructing
an idealized set of simulated observations for a fiducial model, we forecast
the likely constraints that might be possible for a variety of proposed surveys
which are assumed to be flux limited. We find that Sunyaev-Zel'dovich cluster
surveys can provide vital complementary information to those expected from
surveys for supernovae. We analyse the impact of statistical and systematic
uncertainties and find that they only slightly limit our ability to constrain
the equation of state of the dark energy component.
