CODEX, a high resolution, super-stable spectrograph to be fed by the E-ELT, the most powerful telescope ever conceived, will for the first time provide the possibility of directly measuring the change of the expansion rate of the Universe with time a
nd much more, from the variability of fundamental constants to the search for other earths. A study for the implementation at the VLT of a precursor of CODEX, dubbed ESPRESSO, is presently carried out by a collaboration including ESO, IAC, INAF, IoA Cambridge and Observatoire de Geneve. The present talk is focused on the cosmological aspects of the experiment.
