Extragalactic Magnetic Field and the Highest Energy Cosmic Rays

The strength and spectrum of the extragalactic magnetic field are still unknown. Its measurement would help answer the question of whether galactic fields are purely a primordial relic or were dynamically enhanced from a much smaller cosmological seed field. In this letter, we show that the composition, spectrum, and directional distribution of extragalactic ultrahigh energy cosmic rays with energies above $\simeq {10}^{18}\text{ev}$ can probe the large scale component of the extragalactic magnetic field below the present observational upper limit of ${10}^{-9}$ Gauss. Cosmic ray detectors under construction or currently in the proposal stage should be able to test the existence of the extragalactic magnetic fields on scales of a few to tens of Mpc and strengths in the range $\simeq {10}^{-10}-{10}^{-9}$ Gauss.