We use the X-ray power spectrum of the ROSAT all-sky survey in the R6 band ( \approx 0.9-1.3 keV ) to set an upper limit on the galaxy cluster power spectrum .
The cluster power spectrum is modelled with a minimum number of robust assumptions regarding the structure of the clusters .
The power spectrum of ROSAT sets an upper limit on the \Omega _ { m } - \sigma _ { 8 } plane which excludes all the models with \sigma _ { 8 } above \sigma _ { 8 } = 0.5 \Omega _ { m } ^ { -0.38 } in a flat \Lambda CDM universe .
We discuss the possible sources of systematic errors in our conclusions , mainly dominated by the assumed L _ { x } - T relation .
Alternatively , this relation could be constrained by using the X-ray power spectrum , if the cosmological model is known .
Our conclusions suggest that only models with a low value of \sigma _ { 8 } ( \sigma _ { 8 } < 0.8 for \Omega _ { m } = 0.3 ) may be compatible with our upper limit .
We also find that models predicting lower luminosities in galaxy clusters are favoured .
Reconciling our cosmological constraints with these arising by other methods might require either a high entropy floor or wide-spread presence of cooling flows in the low-redshift clusters .