Discrete source counts and the rotation of the local universe in hierarchical cosmology

Attention is given to four reasons for believing that the upper limit on the rotation of the Universe ω set by isotropy of the 3 K background may not be appropriate to the local system because of its hierarchical structure. In particular, recent work of Rubin et al. (1973) on the anisotropy of Hubble's parameter (H) as determined by certain galaxies is examined. The anisotropy in H is a 1st order harmonic effect, inconsistent with an origin in an acceleration of the expansion of the Universe, but explicable as being due to a large peculiar velocity of the Local Group. This compromises limits set on ω by isotropy of the 3 K field, as does the realization that only weak limits can be set if the last-scattering surface (zsub(*)) is not zsub(*)→infinity but is at small z sub(*) (as expected in a hierarchy). In a rotating Universe, the 3-spaces of constant density cannot be orthogonal on the world lines of matter: a number test of Godell based on this is generalized and applied (after consideration of Galactic obscuration) to the local Universe, by taking data on clusters of galaxies from the Abell and Zwicky catalogues. Data from the former give only a marginally significant result for the component (ω1) of ω in one direction, but a bootstrap argument is applied which takes significance over from Abell's data (considered as a class of galaxies) to Zwicky's data (taken as a class of clusters) giving a statistically significant result on the hypothesis that clusters are the fundamental units of the Universe. (Auth.)