The Cosmological Implications of the Recent Counts of Radio Sources: II. An Evolutionary Model

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Abstract
The question of whether an isotropic evolutionary universe can fit the results of the Cambridge survey is investigated. In Paper I it was shown that, for this to be possible at all, the average radio power of the sources must decrease with advancing epoch at a rate exceeding a minimum value related to the time dependence of the number density of the sources. In the present paper attention is confined to the special family of cosmological models which are spatially flat and in which the space expansion factor R ( t ) is equal to t n ( n constant). In the analysis two special assumptions, suggested by general relativity, are made regarding the evolution of the power of radio sources. These lead to the result that for the special models considered the emissivity of space due to the radio sources varies inversely as t3 approximately, at least for the range of cosmic time relevant to the Cambridge survey. The evolutionary theory implies that n is confined to the range 1/2 < n < 2/3, and for agreement with conditions established in I is restrictive of the time dependence of the density of the sources. On this basis, neglecting any dispersion in the intrinsic power of the sources, it is found that a model for which n is less than, but very close to, the value 2/3 will yield a log N − log S graph in close agreement with the Cambridge observations. This model has an acceleration parameter equal to −0.5 which also agrees within error with the value recently found by Baum. Taking the reciprocal of the Hubble constant as 1.3 × 10 10 years, this model's present age would be 8.7 × 10 9 years. The theory indicates that, at the epoch corresponding to the peak of the observed log ( N / N0 ) − log S curve, the mean power of the radio sources would have been about 10 times greater than the present value.

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