The response of primordial abundances to a general modification of   $G_{\rm N}$ and/or of the early universe expansion rate
  We discuss the effects of a possible time variation of the Newton constant $G_{\rm N}$ on light elements production in Big Bang Nucleosyntesis (BBN). We provide analytical estimates for the dependence of primordial abundances on the value of the Newton constant during BBN. The accuracy of these estimates is then tested by numerical methods. % Moreover, we determine numerically the response of each element to an arbitrary time-dependent modification of the early universe expansion rate. Finally, we determine the bounds on possible variations of $G_{\rm N}$ which can be obtained from the comparison of theoretical predictions and observational data. 
C. Bambi, M. Giannotti, and F. L. Villante