  The Cherenkov Telescopic Array (CTA), the next-generation ground-based
gamma-ray observatory, will have unprecedented sensitivity, providing answers
to open questions in gamma-ray cosmology and fundamental physics. Using
simulations of active galactic nuclei observations foreseen in the CTA Key
Science Program, we find that CTA will measure gamma-ray absorption on the
extragalactic background light with a statistical error below 15% up to the
redshift of 2 and detect or establish limits on gamma halos induced by the
intergalactic magnetic field of at least 0.3 pG. Extragalactic observations
using CTA also demonstrate the potential for testing physics beyond the
Standard Model. The best state-of-the-art constraints on the Lorentz invariance
violation from astronomical gamma-ray observations will be improved at least
two- to threefold. CTA will also probe the parameter space where axion-like
particles can represent a significant proportion - if not all - of dark matter.
Joint multiwavelength and multimessenger observations, carried out together
with other future observatories, will further foster the growth of gamma-ray
cosmology.
