Mathematics – Logic
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........22c&link_type=abstract
Thesis (PH.D.)--THE UNIVERSITY OF MICHIGAN, 1995.Source: Dissertation Abstracts International, Volume: 56-12, Section: B, page:
Mathematics
Logic
Cosmological Constant
Scientific paper
Measuring the density of the universe has been a fundamental problem in cosmology ever since the "Big Bang" model was developed over sixty years ago. In this simple and successful model, the age and eventual fate of the universe are determined by its density, its rate of expansion, and the value of a universal "cosmological constant". Analytic models suggest that many properties of galaxy clusters are sensitive to cosmological parameters. In this thesis, I use N-body simulations to examine cluster density profiles, abundances, and degree of subclustering to test the feasibility of using them as cosmological tests. The dependence on both cosmology and initial density field is examined, using a grid of cosmologies and scale-free initial power spectra P(k)~ k n. Einstein-deSitter ( Omegao=1), open ( Omegao=0.2 and 0.1) and flat, low density (Omegao=0.2, lambdao=0.8) models are studied, with initial spectral indices n=-2, -1 and 0. Of particular interest are the results for cluster profiles and substructure. The average density profiles are well fit by a power law p(r)~ r ^{-alpha} for radii where the local density contrast is between 100 and 3000. There is a clear trend toward steeper slopes with both increasing n and decreasing Omegao, with profile slopes in the open models consistently higher than Omega=1 values for the range of n examined. The amount of substructure in each model is quantified and explained in terms of cluster merger histories and the behavior of substructure statistics. The statistic which best distinguishes models is a very simple measure of deviations from symmetry in the projected mass distribution --the "Center-of-Mass Shift" as a function of overdensity. Some statistics which are quite sensitive to substructure perform relatively poorly as cosmological indicators. Density profiles and the Center-of-Mass test are both well-suited for comparison with weak lensing data and galaxy distributions. Such data are currently being collected and should be available within the next few years. At that time the predictions described here can be used to set useful cosmological constraints.
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