  In the context of cold dark matter (CDM) cosmological models, we have
simulated images of the brightness temperature fluctuations in the cosmic
microwave background (CMB)sky owing to the Sunyaev Zel$^{\prime}$dovich (S-Z)
effect in a cosmological distribution of clusters. We compare the image
statistics with recent ATCA limits on arcmin-scale CMB anisotropy. The S-Z
effect produces a generically non-Gaussian field and we compute the variance in
the simulated temperature-anisotropy images, after convolution with the ATCA
beam pattern, for different cosmological models. All the models are normalised
to the 4-year {\it COBE} data. We find an increase in the simulated-sky
temperature variance with increase in the cosmological density parameter
$\Omega_0$. A comparison with the upper limits on the sky variance set by the
ATCA appears to rule out our closed-universe model: low-$\Omega_0$
open-universe models are preferred. The result is independent of any present
day observations of $\sigma_8$.
