Ultrahigh energy cosmic ray probes of large scale structure and magnetic fields

We study signatures of a structured universe in the multi-pole moments, auto-correlation function, and cluster statistics of ultrahigh energy cosmic rays above ${10}^{19}\mathrm{eV}.$ We compare scenarios where the sources are distributed homogeneously or according to the baryon density distribution obtained from a cosmological large scale structure simulation. The influence of extragalactic magnetic fields is studied by comparing the case of negligible fields with fields expected to be produced along large scale shocks with a maximal strength consistent with observations. We confirm that strongly magnetized observers would predict considerable anisotropy on large scales, which is already in conflict with current data. In the best fit scenario only the sources are strongly magnetized, although deflection can still be considerable, of order $20°$ up to ${10}^{20}\mathrm{eV},$ and a pronounced GZK cutoff is predicted. We then discuss signatures for future large scale full-sky detectors such as the Pierre Auger and EUSO projects. Auto-correlations are sensitive to the source density only if magnetic fields do not significantly affect propagation. In contrast, for a weakly magnetized observer, degree scale auto-correlations below a certain level indicate magnetized discrete sources. It may be difficult even for next generation experiments to distinguish between structured and unstructured source distributions.