  In a previous paper (Serna & Alimi 1996), we have pointed out the existence
of some particular scalar-tensor gravity theories able to relax the
nucleosynthesis constraint on the cosmic baryonic density. In this paper, we
present an exhaustive study of primordial nucleosynthesis in the framework of
such theories taking into account the currently adopted observational
constraints. We show that a wide class of them allows for a baryonic density
very close to that needed for the universe closure. This class of theories
converges soon enough towards General Relativity and, hence, is compatible with
all solar-system and binary pulsar gravitational tests. In other words, we show
that primordial nucleosynthesis does not always impose a very stringent bound
on the baryon contribution to the density parameter.
