Anisotropies of Diffusive Ultra-high Energy Cosmic Rays in $f(R)$ Gravity Theory

Understanding the anisotropy of ultra high-energy cosmic rays (UHECRs) is crucial for unraveling the origins and propagation mechanisms of these enigmatic particles. In this work, we studied the dipolar anisotropy of UHECRs in the diffusive regime by considering three cosmological models: the standard $\Lambda$CDM model, $f(R)$ gravity power-law model and the Starobinsky model. This work aims to see the role of the $f(R)$ gravity theory in understanding the anisotropy of UHECRs without condoning the standard cosmology. We found that the amplitude of the dipolar anisotropy is sensitive to these cosmological models, with the $f(R)$ power-law model predicting the largest amplitude, while the $\Lambda$CDM model predicting the smallest amplitude at most of the energies in the range considered. The predicted amplitude of the Starobinsky model lies within the range of the $\Lambda$CDM one. This work not only provides a way for exploration of UHECRs anisotropy within different cosmological contexts but also may pave the way for new avenues of research at the intersection of high-energy astrophysics.