Big bang nucleosynthesis and tensor-scalar gravity

Big bang nucleosynthesis (BBN) is studied within the framework of a two-parameter family of tensor-scalar theories of gravitation, with a nonlinear scalar-matter coupling function a () =a₀+₀ (-₀) +12 (-₀) ^2. We run a BBN code modified by tensor-scalar gravity, and impose that the theoretically predicted BBN yields of deuterium, helium and lithium lie within some conservative observational ranges. It is found that large initial values of a () (corresponding to cosmological expansion rates, for temperatures higher than 1 MeV, much larger than standard) are compatible with observed BBN yields. However, the BBN-inferred upper bound on the cosmological baryon density is insignificantly modified by considering tensor-scalar gravity. Taking into account the effect of e^+e^- annihilation together with the subsequent effect of the matter-dominated era (which both tend to decouple from matter), we find that the present value of the scalar coupling, i. e. , the present level of deviation from Einstein's theory, must be, for compatibility with BBN, smaller than ₀^210^-6. 5^-1 (₌₀ₓₓ₄ₑh^2/0. 15) ^-3/2 when 0. 5.