Variation of the fine structure constant and the electron mass at early
  Universe
  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. We
analyze the details of the recombination physics, including helium
recombination, in order to find the dependences of the physical quantities on
the fundamental constants. Using up-to-date CMB data, and the final 2dFGRS
power spectrum, we set limits to the possible variation of the constants at
recombination. We analyze the variation of $\alpha$ and $m_e$ independently,
and the case in which both variations are allowed, fitting also a set of
cosmological parameters. We find a fenomenological relationship between the
variation of $\alpha$ and the variation of $m_e$, between decoupling and
present time. We analyze the Barrow-Magueijo fenomenological model, which
propose a variation in the electron mass induced by changes in a space-time
scalar field. We present improved solutions and we estimate the model
parameters using bounds on the variation of the electron mass at different
cosmic times. On the other hand, from results of experiments that test the Weak
Equivalence Principle, we find a limit for the model's parameter, that comes
from the variation of the electron mass induced by spatial variations of the
scalar field. By comparing both limits, we arrive at the conclusion that the
model 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 the
electron mass does not induce observable changes on the radii. We present a
local and independent bound on the variation of $\alpha$, obtained from very
general statements. (TEXT IN SPANISH)
