Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; Univ Sci & Technol China, Interdisciplinary Ctr Theoret Study, Hefei 230026, Peoples R China
; Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
We discuss the threshold anomaly in ultrahigh energy cosmic ray physics by assuming that the matter world just be a perturbation of a de Sitter universe, which is consistent with the recent astronomical observations: about two-thirds of the whole energy in the Universe is contributed by a small positive cosmological constant. One-particle states are presented explicitly. It is noticed that the dispersion relation of free particles is dependent on the degrees of freedom of angular momentum. This fact can be regarded as the effects of the cosmological constant on kinematics of particles.