Varying constants and dark energy with the E-ELT

The observational possibilities enabled by an ultra-stable CODEX-like spectrograph at the E-ELT will open new doors in the characterisation of the nature of Dark Energy. Indeed, it will provide measurements of a so far unexplored redshift-range ($2<z<5$) and will carry out simultaneously cosmological tests such as the Sandage-Loeb test and precision tests of the standard model. Here we will illustrate how, with these abilities, such spectrographs - alone or in synergy with other facilities - will manage to constrain cosmological scenarios and test classes of models that would otherwise be difficult to distinguish from the standard $\Lambda{\rm CDM}$ paradigm.