Ultra-high-energy physics is about to enter a new era thanks to the impressive results of experiments such as the Large
High Altitude Air Shower Observatory, detecting photons of up to 1.4 × 1015 eV (PeV scale). These new results could be used to
test deviations with respect to special relativity. While this has been already explored within the approach of Lorentz Invariance
Violation theories, in this work we consider, for the first time, modifications due to a relativistic deformed kinematics (which appear
in Doubly Special Relativity, or DSR, theories). In particular, we study the mean free path of very high-energy photons due to
electron-positron pair creation when interacting with low-energy photons of the cosmic microwave background. Depending on the
energy scale of the relativistic deformed kinematics, present (or near future) experiments can be sensitive enough to be able to
identify deviations from special relativity.
