Relativistic hierarchical cosmology

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)α¹ F ^−3/2, hierarchical models with ϱ = ϱ₀ r ⁻² haveN(>F,ν)∝F ^−1/2 (Section 1). Since the observed dependency isN(>F,ν)∝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),$\dot k$(t) andR (Section 7) leads one to suggest that ak=0,$\dot k$=0 hierarchy with Λ≠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.