  We study here the effect of a varying G on the evolution of the early
Universe and, in particular, on primordial nucleosynthesis. This variation of G
is modelled using the Brans-Dicke theory as well as a more general class of
scalar-tensor theories. Modified nucleosynthesis codes are used to investigate
this effect and the results obtained are used to constrain the parameters of
the theories. We extend previous studies of primordial nucleosynthesis in
scalar-tensor theories by including effects which can cause a slow variation of
G during radiation domination and by including a late-time accelerating phase
to the Universe's history. We include a brief discussion on the epoch of
matter-radiation equality in Brans-Dicke theory, which is also of interest for
determining the positions of the cosmic microwave background power-spectrum
peaks.
