Relativistic hierarchical cosmology |
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| Authors: | Paul S Wesson |
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| Institution: | (1) St. John's College, and Institute of Astronomy, Cambridge University, Cambridge, England |
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| Abstract: | While Euclidean models with uniform matter density have a number of radio sources of flux density greater thanF at frequencyv that varies asN(>F, v) 1
F
–3/2, hierarchical models with  = 0
r
–2 haveN(>F, ) F
–1/2 (Section 1). Since the observed dependency isN(>F,)F
–1.8, severe density and/or luminosity evolution must be present in a workable hierarchical cosmology (Section 2). The same argument applies (Section 3) to the number of sources of apparent luminosity greater thanl,N(>l) and (Section 4) to the number of sources within redshift distancez from the local origin. To give agreement with empirical data demandsq
o=+1 and large first and second derivatives with respect to time of the number source density (Section 5). The adoption ofq
o=+1 allows one to show (Section 6) that a Lemaitre-type hierarchical Universe with a long coasting or waiting time can give agreement with observations of the numbers of QSO's etc. if the age of the Universe is more than 1013 yr. The dependence of the effective Hubble parameter onk(t),
(t) andR (Section 7) leads one to suggest that ak=0,
=0 hierarchy with   0 might be the simplest acceptable form of model Universe. Section 8 (Conclusion) points out that further data on source count anisotropies should allow the component levels of the hierarchy to be delineated. |
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| Keywords: | |
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