Light Elements and the Isotropy of the Universe

Nucleosynthesis in homogeneous Bianchi-type universes admitting Robertson–Walker solutions is investigated. The requirement that helium and deuterium are synthesized cosmologically in the abundance range observed is shown to constrain the ratio of the shear to the expansion rate, $$(\sigma/\theta)_{0},$$ of the Universe today more severely than does the measured isotropy of the microwave background radiation. Rotation is shown to have a negligible effect upon nucleosynthesis and in particular if the Universe were Bianchi I then the abundances $$X(\text{He}^{4}) = 0 \cdot 29 \pm 0 \cdot 04, X(\text{D}) \sim 2.10^{-5}$$ indicate that $$(\sigma/\theta)_{0} \lesssim 4 \cdot 8. 10^{-12}.$$ The local shear induced by large scale density perturbations is also considered together with some qualitative discussion of the physical effects of inhomogeneity.