Observational strategies for varying constants with ESPRESSO and ELT-HIRES

The observational evidence for the acceleration of the universe demonstrates that canonical theories of cosmology and particle physics are incomplete, if not incorrect. Several few-sigma hints of new physics, discussed in this workshop, are arguably smoke without a smoking gun. Forthcoming high-resolution ultra-stable spectrographs will play a crucial role in this quest for new physics, by enabling a new generation of precision consistency tests. Here we focus on astrophysical tests of the stability of nature's fundamental couplings, discussing the improvements that can be expected with ESPRESSO and ELT-HIRES and their impact on fundamental cosmology. We find that the current E-ELT configuration has the potential to constrain dark energy more strongly than standard surveys with thousands of low-redshift ($z<2$) supernovas.