Propagation and Fluxes of Ultra High Energy Cosmic Rays in f(R) Gravity Theory

We study the effect of diffusion of ultra-high energy cosmic ray (UHECR) protons in the presence of turbulent magnetic fields in the light of the $f(R)$ theory of gravity. The $f(R)$ theory of gravity is a successful modified theory of gravity in explaining the various aspects of the observable Universe including its current state of expansion. Here, we consider the two most studied $f(R)$ gravity models, viz., the power-law model and the Starobinsky model. For these two models, the diffusive character of the propagation of UHECR protons is explored in terms of their density enhancement (a measure of how the density of UHECRs changes due to their diffusion and interactions in the intergalactic medium). Ankle, instep, and Greisen-Zatsepin-Kuzmin cutoff are spectral characteristics that extragalactic UHECRs acquire when they propagate through the cosmic microwave background. All these characteristics are analysed through the diffusive flux as well as its modification factor. We compare the UHECR protons spectra calculated for the considered $f(R)$ gravity models with the available data of the Telescope Array and Pierre Auger Observatory. Both models of $f(R)$ gravity predict energy spectra of UHECRs with all experimentally observed features, which lay well within the range of combined data of both experiments. However, this work is only to investigate the possible effects of $f(R)$ gravity theory on the UHECRs propagation, using pure proton composition as a simplified case study. At this stage, our results cannot be used to favour or disfavour the $f(R)$ cosmology over the $\Lambda$CDM cosmology.