  The observational evidence for the recent acceleration of the universe
demonstrates that canonical theories of cosmology and particle physics are
incomplete (or possibly incorrect) and that new physics is out there, waiting
to be discovered. A crucial task for the next generation of astrophysical
facilities is to search for, identify and ultimately characterise this new
physics. I outline the theoretical arguments pointing to this new physics, and
then discuss some unique contributions of the ELTs towards this endeavour,
including tests of the stability of nature's fundamental couplings, tests of
the behaviour of gravity in the strong-field regime, and mapping the expansion
history of the universe in the deep matter era, by both direct and indirect
means. I also briefly highlight how the ELTs can optimally complement other
planned ground and space facilities, and stress the requirements that these
searches impose on the instruments currently being built or developed.
