  The Cherenkov Telescope Array (CTA) is a project for a next-generation
observatory for very high energy (GeV-TeV) ground-based gamma-ray astronomy,
currently in its design phase, and foreseen to be operative a few years from
now. Several tens of telescopes of 2-3 different sizes, distributed over a
large area, will allow for a sensitivity about a factor 10 better than current
instruments such as H.E.S.S, MAGIC and VERITAS, an energy coverage from a few
tens of GeV to several tens of TeV, and a field of view of up to 10 deg. In the
following study, we investigate the prospects for CTA to study several science
questions that influence our current knowledge of fundamental physics. Based on
conservative assumptions for the performance of the different CTA telescope
configurations, we employ a Monte Carlo based approach to evaluate the
prospects for detection. First, we discuss CTA prospects for cold dark matter
searches, following different observational strategies: in dwarf satellite
galaxies of the Milky Way, in the region close to the Galactic Centre, and in
clusters of galaxies. The possible search for spatial signatures, facilitated
by the larger field of view of CTA, is also discussed. Next we consider
searches for axion-like particles which, besides being possible candidates for
dark matter may also explain the unexpectedly low absorption by extragalactic
background light of gamma rays from very distant blazars. Simulated
light-curves of flaring sources are also used to determine the sensitivity to
violations of Lorentz Invariance by detection of the possible delay between the
arrival times of photons at different energies. Finally, we mention searches
for other exotic physics with CTA.
