Model-Universes in Hoyle's Cosmology

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Abstract
A systematic study of the permissible model-universe and their physical properties of Hoyle-Narlikar's cosmological equations is carried out by comparing them with those in the relativistic cosmology. It is revealed then that the models can be classified into three different types (A1), (A2) and (B). The type (A1) consists of the steady-state model and the two steady-state like models which correspond to the three alternative Robertson-Walker metrics for the de Sitter empty space-time. The type (A2) is characterized by the fact that, except for the matter density, the temporal behaviors of Hubble's expansion parameter and the deceleration parameter can be identified with those in the relativistic pressure-free models with a positive cosmic constant. Any model of the type (B) satisfies the conservation of total mass, just like the relativistic pressure-free models, and is very similar to the case of vanishing cosmic constant, but free from the initial singular event characteristic of the latter case. The problem of comparison with observational data concerning the redshift-magnitude relation and the time-scale criterion is also touched upon briefly.

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