Evolution of Large Scale Structure { Garching , August 1998 DETERMINING COSMOLOGICAL PARAMETERSFROM CLUSTER

We show that the evolution of the number density of rich clusters of galaxies breaks thèclassical' degeneracy between (the cosmological mass density parameter of the universe) and 8 (The amplitude of mass uc-tuations on 8Mpc scale) that follows from the observed present-day cluster abundance. The evolution of cluster abundance thus provides a determination of each of these parameters independently. The evolution of massive clusters is strong in = 1, low 8 models (such as the standard biased cold dark matter model with 8 0.5), where the number density of clusters decreases sharply (by a factor 10 2 ? 10 5 , depending on cluster mass) from redshift z = 0 to z 0.5; the same clusters show only mild evolution in low-, high-8 models, where the decease is only a factor of 10. This implies that nding even a few very massive clusters at z 0.5 ? 1 is inconsistent with = 1 models, where such clusters would be very rare { these massive systems have not yet formed at these redshifts. This diagnostic provides a most powerful constraint on and 8. Using observations of clusters to z 1 we nd only mild evolution in the observed cluster abundance. The existence of massive clusters at z > 0:5 is shown to be highly inconsistent with = 1 models, where only 10 ?3 to 10 ?5 such clusters are expected as compared with the several clusters observed. Using the available data we nd w 0.2 (+0.15, ?0.1) and 8 w 1.2(0.3). This result implies a low-density un-biased universe, with mass approximately tracing light on large scales.