Time variation of the electron mass in the early universe and the Barrow-Magueijo model

We put limits on the time variation of the electron mass in the early universe using observational primordial abundances of D, He4 and Li7, recent data from the Cosmic Microwave Background and the 2dFGRS power spectrum. Furthermore, we use these constraints together with other astronomical and geophysical bounds from the late universe to test Barrow-Magueijo's model for the variation in m_e. From our analysis we obtain -0.615 < G\omega/c^4 < -0.045 (3\sigma interval) in disagreement with the result obtained in the original paper.