Constraints on structure formation models from Sunyaev-Zel'dovich Effect

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${}^{\mathrm{\prime }}$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 ${\mathrm{\Omega }}_0$. A comparison with the upper limits on the sky variance set by the ATCA appears to rule out our closed-universe model: low-${\mathrm{\Omega }}_0$ open-universe models are preferred. The result is independent of any present day observations of ${\sigma }_8$.