No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

A number of different ways of using galaxy clusters to provide information concerning fundamental cosmological parameters are considered. Using the observed local cluster X-ray temperature function in conjunction with the Press-Schechter formalism, the normalisation of a CDM power spectrum is found to be σ(_8) = (0.52 ± 0.04)Ω(_o)(^-0.46+0.10Ωo) if Ʌ(_o) = 0 or σ(_8) = (0.52 ± 0.04)Ω(_o)(^-0.52+0.13Ωo) if Ʌ(_o) = 1 — Ω(_0). This result is employed to provide detailed predictions for the abundance of clusters at high redshift, and the differences between predictions for various cosmologies are emphasised. New tests using available high-redshift cluster data are presented. For the adopted power spectrum normalisation, it is found that an Ω(_o) = 0.3, Ʌ(_o) = 0 cosmology vastly overpredicts the number of clusters that were actually found with 0.4 < z < 0.6 in the Extended Medium Sensitivity Survey. The rapid variation in the expected abundance with both σ(_8) and the assumed scatter in the L(_x) – T_x) relation limits the significance of this result, but this model is still ruled out at the ~ 95% confidence level. Order statistics are utilised to calculate the probability of finding extremely massive clusters at high redshifts. With presently available observations, no interesting upper limit can yet be placed on Ω(_o). Systematic variations in the cluster-cluster correlation length calculated using numerical simulations and resulting from the definition of clusters, the chosen σ(_8), the mean intercluster separation and whether or not redshift space distortions are included, are found to exceed the statistical errors on the measurements. Although the uncertainty in ε(_cc) derived from an ensemble of 10 Standard CDM simulations is not sufficient at large separations to remove the discrepancy between this model and results from the APM Cluster Survey, this does suggest that the level at which such a scenario has previously been rejected using ε(_cc) should be significantly reduced. Details and a few tests of a procedure for improving mass and spatial resolution in cosmological simulations are presented. After showing that a coarse-sampling technique can be used to represent the large-scale forces sufficiently accurately, the method is then used to perform ten simulations of clusters forming in an Ω(_o) = 0.3, Ʌ(_o) = 0.7 CDM cosmology. To incorporate non-radiative gas, an SPH code adapted to work on a GRAPEsupercomputer is used. The resulting clusters are found to have virial radii in good agreement with the predictions of the spherical collapse model, dark matter density profiles well described by the 'NFW formula and isothermal central gas components, with temperatures dropping by a factor of ~ 2 near the virial radius. The evolution of these properties is studied as well as that of the bulk quantities describing the clusters, with particular reference to the β parameters relating cluster gas temperatures with virial mass or velocity dispersion. Slightly greater evolution in the luminosity is seen than in previous Ω(_o) = 1 simulations, suggesting that the improved resolution is important. The β parameter relevant to the normalisation of the mass fluctuation spectrum is found to be 0.98 ± 0.07.