2015ApJ...806..184D

Accretion of gas during the large-scale structure formation has been thought to give rise to shocks that can accelerate cosmic rays. This process then results in an isotropic extragalactic gamma-ray emission contributing to the extragalactic gamma-ray background (EGRB) observed by Fermi-LAT. Unfortunately, this emission has been difficult to constrain and thus presents an uncertain foreground to any attempts to extract a potential dark matter signal. Recently, IceCube has detected high-energy isotropic neutrino flux that could be of an extragalactic origin. In general, neutrinos can be linked to gamma rays since cosmic-ray interactions produce neutral and charged pions where neutral pions decay into gamma rays, while charged pions decay to give neutrinos. By assuming that isotropic high-energy IceCube neutrinos are entirely produced by cosmic rays accelerated in accretion shocks during the process of structure formation, we obtain the strongest constraint to the gamma-ray emission from large-scale structure formation (strong) shocks and find that they can make at best ∼20% of the EGRB, corresponding to neutrino flux with spectral index α_ν= 2, or ∼10% for spectral index α_ν= 2.46. Since typical objects where cosmic rays are accelerated in accretion shocks are galaxy clusters, observed high-energy neutrino fluxes can then be used to determine the gamma-ray emission of a dominant cluster type and constrain acceleration efficiency, and thus probe the process of large-scale structure formation.