Varying couplings in the early universe: Correlated variations of alpha and G

The cosmic microwave background anisotropies provide a unique opportunity to constrain simultaneous variations of the fine-structure constant alpha and Newton's gravitational constant G. Those correlated variations are possible in a wide class of theoretical models. In this brief paper we show that the current data, assuming that particle masses are constant, give no clear indication for such variations, but already prefer that any relative variations in alpha should be of the same sign of those of G for variations of similar to 1%. We also show that a cosmic complementarity is present with big bang nucleosynthesis and that a combination of current CMB and big bang nucleosynthesis data strongly constraints simultaneous variations in alpha and G. We finally discuss the future bounds achievable by the Planck satellite mission.