Constraints on the scalar-tensor theories of gravitation from primordial nucleosynthesis

We present a detailed calculation of the light element production in the framework of scalar-tensor theories of gravitation. The coupling function ω is described by an appropriate form which reproduces all the possible asymptotic behaviors at early times of viable scalar-tensor cosmological models with a monotonic ω(Φ). This form gives an exact representation for most of the particular theories proposed in the literature, but also a first-order approximation to many other theories. In most scalar-tensor theories, the comparison of our results with current observations implies very strong bounds on the allowed deviation from general relativity (GR). These bounds lead to cosmological models which do not significantly differ from the standard Friedman-Robertson-Walker ones. We have found, however, a particular class of scalar-tensor theories in which the expansion rate of the universe during nucleosynthesis can be very different from that found in GR, while the present value of the coupling function ω is high enough to ensure compatibility with solar-system experiments. In the framework of this class of theories, right primordial yields of light elements can be obtained for a baryon density range much wider (2.8≲${\mathrm{\eta }}_{10}$≲58.7) than in GR. Consequently, the usual constraint on the baryon contribution to the density parameter of the universe can be drastically relaxed (0.01≲${\mathrm{\Omega }}_{\mathit{b}0}$≲1.38) by considering these gravity theories. This is the first time that a scalar-tensor theory is found to be compatible both with primordial nucleosynthesis and solar-system experiments while implying cosmological models significantly different from the FRW ones. © 1996 The American Physical Society.