The amplitude of density perturbations , for the currently-favoured \Lambda CDM 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 .