Abstract
The scale-covariant theory of gravitation, which was proposed by Canutoet al. (1977), assumes that gravitational and atomic units are related by a scalar function of space-time. The cosmology based on this theory can explain very well the 3K radiation, as well as Hubble's redshift law. However, Falik (1979) derived a result from the scale-covariant cosmology which was in conflict with the observed helium abundance. Contrary to Falik, we show in this paper that if we choose a gauge functionβ∼tα and α satisfies the condition −1/3<α<1, the scale-covariant cosmology will be consistent with the observed cosmic-helium abundance. The value α=1/2 has recently been suggested by Canuto and Goldman (1982) on general grounds.
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