Photon Absorption in a Doubly Special Relativity Model with Undeformed Free Propagation and Total Momentum Conservation

The lack of a dynamical framework within doubly special relativity theories has impeded the development of a corresponding phenomenology of modified interactions. In this work we show that in a model based on the classical basis of $\kappa$-Poincaré and total momentum conservation, one has a well-defined cross section of the photon-photon annihilation process, once a prescription for the channel treatment is set. The modification of the interaction can lead to observable effects in the opacity of the Universe to very high-energy gamma rays when the gamma-ray energy approaches the energy scale of the deformation. The magnitude and observability of this deformation are examined as functions of the gamma-ray energy and source distance.