  In this thesis we study the influence of a possible variation of fundamental
"constants" on the process of Big Bang Nucleosynthesis (BBN). Our findings are
combined with further studies on variations of constants in other physical
processes to constrain models of grand unification (GUT) and quintessence. We
will find that the 7Li problem of BBN can be ameliorated if one allows for
varying constants, where especially varying light quark masses show a strong
influence. Furthermore, we show that recent studies of varying constants are in
contradiction with each other and BBN in the framework of six exemplary GUT
scenarios, if one assumes monotonic variation with time. We conclude that there
is strong tension between recent claims of varying constants, hence either some
claims have to be revised, or there are much more sophisticated GUT relations
(and/or non-monotonic variations) realized in nature. The methods introduced in
this thesis prove to be powerful tools to probe regimes well beyond the
Standard Model of particle physics or the concordance model of cosmology, which
are currently inaccessible by experiments. Once the first irrefutable proofs of
varying constants are available, our method will allow for probing the
consistency of models beyond the standard theories like GUT or quintessence and
also the compatibility between these models.
