  The Cherenkov Telescope Array (CTA) is the next generation ground-based
observatory for $\gamma$-ray astronomy at energies above 30 GeV. Thanks to its
unique capabilities, CTA observations will address a plethora of open questions
in astrophysics ranging from the origin of cosmic messengers to the exploration
of the frontiers of physics. In this note, we present a comprehensive
sensitivity study to assess the potential of CTA to measure the $\gamma$-ray
absorption on the extragalactic background light (EBL), to constrain or detect
intergalactic magnetic fields (IGMFs), and probe physics beyond the Standard
Model such as axion-like particles (ALPs) and Lorentz invariance violation
(LIV), which could modify the $\gamma$-ray spectra features expected from EBL
absorption. Our results suggest that CTA will have unprecedented sensitivity to
detect IGMF signatures and will probe so-far unexplored regions of the LIV and
ALP parameter space. Furthermore, an indirect measurement of the EBL and of its
evolution will be performed with unrivaled precision.
