Detecting ultra-high energy cosmic ray anisotropies through
  cross-correlations
  We propose an observable for ultra-high energy cosmic ray (UHECR) physics:
the harmonic-space cross-correlation power spectrum between the arrival
directions of UHECRs and the large-scale cosmic structure mapped by galaxies.
This cross-correlation has not yet been considered in the literature, and it
permits a direct theoretical modelling of the main astrophysical components. We
describe the expected form of the cross-correlation and show how, if the
distribution of UHECR sources trace the large-scale cosmic structure, it could
be easier to detect with current data than the UHECR auto-correlation.
Moreover, the cross-correlation is more sensitive to UHECR anisotropies on
smaller angular scales, more robust to systematic uncertainties, and it could
be used to determine the redshift distribution of UHECR sources, making it a
valuable tool in determining their origins and properties.
