Ultra - high energy cosmic rays threshold in Randers - Finsler space

Kinematics in Finsler space is used to study the propagation of ultra high energy cosmic rays particles through the cosmic microwave background radiation. We find that the GZK threshold is lifted dramatically in Randers-Finsler space. A tiny deformation of spacetime from Minkowskian to Finslerian allows more ultra-high energy cosmic rays particles arrive at the earth. It is suggested that the lower bound of particle mass is related with the negative second invariant speed in Randers-Finsler space. PACS numbers: 03.30.+p, 11.30.Cp, 98.70.Sa [email protected] [email protected] 1 Decades ago, Greisen, Zatsepin and Kuz’min (GZK) [1] discussed the propagation of the ultra-high energy cosmic rays (UHECR) particles through the cosmic microwave background radiation (CMBR) [2]. Due to photopion production process by the CMBR, the UHECR particles will lose their energies drastically down to a theoretical threshold (about 5× 10eV). That is to say, the UHECR particles which their energy beyond the threshold can not be observed[3]. This strong suppression is called GZK cutoff. However hundreds of events with energies above 10eV and about 20 events above 10eV have been observed[4]. To explain this puzzle, one general accepted hypothesis is that the Lorentz Invariance (LI) is violated[5]. The violation of the LI and the Planck scale physics have long been suggested as possible solutions of the cosmic rays threshold anomalies[5]. LI is one of the foundations of the Standard model of particle physics. Coleman and Glashow have set up a perturbative framework for investigating possible departures of local quantum field theory from LI[6, 7]. In a different approach, Cohen and Glashow suggested [8] that the exact symmetry group of nature may be isomorphic to a subgroup SIM(2) of the Poincare group. The mere observation of ultra-high energy cosmic rays and analysis of neutrino data give an upper bound of 10 on the Lorentz violation[9]. In fact, Gibbons, Gomis and Pope[10] showed that the Finslerian line element ds = (ημνdx dx)(nρdx ) is invariant under the transformations of the group DISIMb(2). The very special relativity is a Finsler geometry. Recently, we proposed a gravitational field equation in Berwald-Finsler space[11].