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The observational evidence for the recent acceleration of the universedemonstrates that canonical theories of cosmology and particle physics areincomplete (or possibly incorrect) and that new physics is out there, waitingto be discovered. A crucial task for the next generation of astrophysicalfacilities is to search for, identify and ultimately characterise this newphysics. I outline the theoretical arguments pointing to this new physics, andthen discuss some unique contributions of the ELTs towards this endeavour,including tests of the stability of nature's fundamental couplings, tests ofthe behaviour of gravity in the strong-field regime, and mapping the expansionhistory of the universe in the deep matter era, by both direct and indirectmeans. I also briefly highlight how the ELTs can optimally complement otherplanned ground and space facilities, and stress the requirements that thesesearches impose on the instruments currently being built or developed.

Fundamental Physics and Cosmology in the Extremely Large Telescopes Era