Mathematics – Logic
Scientific paper
Jan 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999elss.conf..291b&link_type=abstract
"Evolution of large scale structure : from recombination to Garching /edited by A. J. Banday, R. K. Sheth, L. N. da Costa. Garch
Mathematics
Logic
Scientific paper
I show that the evolution of the number density of rich clusters of galaxies breaks the 'classical' degeneracy between Omega (the cosmological mass density parameter of the universe) and sigma-8 (the amplitude of mass fluctuations 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 Omega=1, low-sigma-8 models (such as the standard biased cold dark matter model with sigma-8 ~ 0.5), where the number density of clusters decreases sharply (by a factor ~102- 105, depending on cluster mass) from redshift z=0 to z ~ 0.5; the same clusters show only mild evolution in low-Omega, high-sigma-8 models, where the decrease is only a factor of ~10. This implies that finding even a few very massive clusters at z ~ 0.5-1 is inconsistent with Omega=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 Omega and sigma-8. Using observations of clusters to z ~ 1 we find only mild evolution in the observed cluster abundance. The existence of massive clusters at z > 0.5 is shown to be highly inconsistent with Omega=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 find Omega=~ 0.25 (+0.2, -0.1) and sigma-8 =~ 1 (+-0.25). This result implies a low-density un-biased universe, with mass approximately tracing light on large scales.
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