  Ultra high energy cosmic rays (UHECRs) may interact with photon backgrounds
and thus the universe is opaque to their propagation. Many Lorentz Invariance
Violation (LIV) theories predict a dilation of the expected horizon from which
UHECRs can arrive to Earth, in some case even making the interaction
probability negligible. In this work, we investigate this effect in the context
of the LIV theory that goes by the name of Homogeneously Modified Special
Relativity (HMSR). In this work, making use of a specifically modified version
of the Sim- Prop simulation program in order to account for the modifications
introduced by the theory to the propagation of particles, the radius of the
proton opacity horizon (GZK sphere), and the attenuation length for the
photopion production process are simulated and the modifications of these
quantities introduced by the theory are studied.
