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In this thesis, we focus on the study of the variation of the electron mass$m_e$, and the fine structure constant $\alpha$, at different cosmic times. Weanalyze the details of the recombination physics, including heliumrecombination, in order to find the dependences of the physical quantities onthe fundamental constants. Using up-to-date CMB data, and the final 2dFGRSpower spectrum, we set limits to the possible variation of the constants atrecombination. We analyze the variation of $\alpha$ and $m_e$ independently,and the case in which both variations are allowed, fitting also a set ofcosmological parameters. We find a fenomenological relationship between thevariation of $\alpha$ and the variation of $m_e$, between decoupling andpresent time. We analyze the Barrow-Magueijo fenomenological model, whichpropose a variation in the electron mass induced by changes in a space-timescalar field. We present improved solutions and we estimate the modelparameters using bounds on the variation of the electron mass at differentcosmic times. On the other hand, from results of experiments that test the WeakEquivalence Principle, we find a limit for the model's parameter, that comesfrom the variation of the electron mass induced by spatial variations of thescalar field. By comparing both limits, we arrive at the conclusion that themodel should be ruled-out. Lastly, we reanalyze the effects of the variation of$\alpha$ or $m_e$ upon planetary radii. We explain why the variation of theelectron mass does not induce observable changes on the radii. We present alocal and independent bound on the variation of $\alpha$, obtained from verygeneral statements. (TEXT IN SPANISH)

Variation of the fine structure constant and the electron mass at early Universe