Dynamical Dark Energy and Variation of Fundamental Constants

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 find 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.