In a previous paper, we pointed out the existence of some particular scalar-tensor gravity theories that are 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 theories allows for a baryonic density very close to that needed for closure of the universe. This class of theories converges soon enough toward 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.
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