We show that the distribution of the sizes and temperatures of clusters can be used to constrain cosmological models .
The size-temperature ( ST ) distribution predicted in a flat Gaussian cluster-abundance-normalized \Omega _ { 0 } = 0.3 model agrees well with the fairly tight ST relation observed .
A larger power-spectrum amplitude \sigma _ { 8 } would give rise to a larger scatter about the ST relation as would a larger value of \Omega _ { 0 } and/or long non-Gaussian high-density tails in the probability density function .
For Gaussian initial conditions , the ST distribution suggests a constraint \sigma _ { 8 } \Omega _ { 0 } ^ { 0.26 } \simeq 0.76 .
The ST relation is expected to get tighter at high redshifts .
In the process , we derive a simple formula for the halo formation-redshift distribution for non-Gaussian models .
We also suggest that the discrepancy between the naive zero-redshift ST relation and that observed may be due , at least in part , to the fact that lower-mass clusters form over a wider range of redshifts .
An Appendix derives an equation for the formation-redshift distribution of halos .