At energies approaching the Planck energy scale 1019 GeV, several
quantum-gravity theories predict that familiar concepts such as Lorentz (LIV)
symmetry can be broken. Such extreme energies are currently unreachable
by experiments on Earth, but for photons traveling over cosmological
distances the accumulated deviations from the Lorentz symmetry may be
measurable using the Cherenkov Telescope Array (CTA).
To study the spectral hardening feature observed in some VHE gamma-ray
blazars, we calculate the reduction of the EBL gamma-gamma opacity due to
the existence of underdense regions along the line of sight to VHE gamma
ray sources and we compared with the possibility of a LIV signature.
Considering the LIV effect, we found that the cosmic opacity for VHE-gamma
rays with energy more than 10 TeV can be strongly reduced. I will further
discuss the impact of LIV on the Compton scattering process, and how
future CTA observations may open an exciting window on studies of the