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 $a({φ}{)=a}₀+{{α}}₀({φ}{-}{{φ}}₀)+1/2{β}({φ}{-}{{φ}}₀{)}².$ 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(φ) (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 φ 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 α₀²10^-6.5β^-1(Ωₘₐₜₜₑᵣh²/0.15)^-3/2 when β0.5.