  Recently conformal Weyl gravity has been considered as a candidate
alternative gravity theory. This fourth-order theory is attractive because it
is the only metric theory of gravity which is invariant under local conformal
transformations of the metric. We calculate the primordial light element
abundances in this theory. The major difference {}from the standard cosmology
is that the universe expands far more slowly throughout the nucleosynthesis
epoch. The production of $^4\rm{He}$ depends strongly on $\eta$, the ratio of
baryons to photons. For $\eta = 10^{-8}$ the mass fraction of $^4{\rm He}$ is
$X_4 \simeq 0.25$ and the number densities relative to hydrogen for $^2{\rm
H}$, $^3{\rm He}$ and $^7{\rm Li}$ are $n(^2{\rm H})/n({\rm H}) \simeq 9\times
10^{-20}$, $n(^3{\rm He})/n({\rm H})\simeq 4 \times 10^{-18}$ and $n(^7{\rm
Li})/n({\rm H}) \simeq 10^{-13}$. This value of $\eta$ corresponds to a baryon
mass density close to the standard model critical density. However, adjusting
$\eta$ to give a reasonable helium yield forces the deuterium and lithium
yields to be small enough that the theory cannot be reconciled with
observations.

Astrophysics;General Relativity and Quantum Cosmology