"I have shown here that there exist relativistic theories in which the GZK cutoff is shifted significantly upward (enough to explain the cosmic-ray puzzle) but there is no preferred class of inertial observers."
~ Giovanni Amelino-Camelia, "Kinematical solution of the UHE-cosmic-ray puzzle without a preferred class of inertial observers", Int.J.Mod.Phys. D12 (2003) 1211-1226, astro-ph/0209232, p. 7
"What could instead accomodate exactly the situation where there is no GZK anomaly but we do find anomalous in vacua despersion? Well [...] you basically could go to the direction I prososed a few years ago, which is allow for departures from Lorentz symmetry but without the emergence of a preferred frame [...] No preferred frame. These turn out to be a much softer class [..] of departures from standard Poincare symmetry [...] They are unable [...] to provide an observably large GZK threshold anomaly.
Despite of what is said in many Doubly Special Relativity papers [...] That's not possible."
~ Giovanni Amelino-Camelia, talk given at the workshop on Experimental Search for Quantum Gravity, pirsa:07110057, min. 26:23