Fundamental Cosmology with the E-ELT

The evidence for the acceleration of the universe shows that canonical theories of cosmology and particle physics are incomplete, and that new physics is out there, waiting to be discovered. Forthcoming high-resolution ultra-stable spectrographs will play a key role in this quest for new physics. Here we focus on astrophysical tests of the stability of nature's fundamental couplings, and by taking existing VLT data as a starting point we discuss how forthcoming improvements (in particular with the E-ELT) will impact on fundamental cosmology.