  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 observed by the Fermi-LAT. Unfortunately
this emission has been difficult to constrain and thus presents an uncertain
foreground to any attempts to extract potential dark matter signal. Recently,
IceCube has detected high-energy isotropic neutrino flux which 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 extragalactic gamma-ray background, corresponding to neutrino flux with
spectral index 2, or ~10% for spectral index 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.
