The power spectrum amplitude from clusters revisited: \sigma_8 using   simulations with preheating and cooling
  The amplitude of density perturbations, for the currently-favoured LambdaCDM cosmology, is constrained using the observed properties of galaxy clusters. The catalogue used is that of Ikebe et al. (2002). The cluster temperature to mass relation is obtained via N-body/hydrodynamical simulations including radiative cooling and preheating of cluster gas, which we have previously shown to reproduce well the observed temperature--mass relation in the innermost parts of clusters (Thomas et al. 2002). We generate and compare mock catalogues via a Monte Carlo method, which allows us to constrain the relation between X-ray temperature and luminosity, including its scatter, simultaneously with cosmological parameters. We find a luminosity-temperature relation in good agreement with the results of Ikebe et al. (2002), while for the matter power spectrum normalization, we find $\sigma_8 = 0.78_{-0.06}^{+0.30}$ at 95 per cent confidence for $\Omega_0 = 0.35$. Scaling to WMAP's central value of $\Omega_0 = 0.27$ would give a best-fit value of $\sigma_8 \simeq 0.9$. 
Pedro T P Viana, Scott T Kay, Andrew R Liddle, Orrarujee Muanwong and   Peter A Thomas