Big Bang Nucleosynthesis ( BBN ) is studied within the framework of a two-parameter family of tensor-scalar theories of gravitation , with nonlinear scalar-matter coupling function a ( \varphi ) = a _ { 0 } + \alpha _ { 0 } ( \varphi - \varphi _ { 0 } ) + \frac { 1 } { 2 } \beta ( \varphi - % \varphi _ { 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 ( \varphi ) ( 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 \varphi 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 \alpha _ { 0 } ^ { 2 } \lesssim 10 ^ { -6.5 } \beta ^ { -1 } ( \Omega _ { matter } h ^ { 2 } / 0.15 % ) ^ { -3 / 2 } when \beta \gtrsim 0.5 .