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 \sim 20 \% of the extragalactic gamma-ray background , corresponding to neutrino flux with spectral index \alpha _ { \nu } = 2 , or \sim 10 \% for spectral index \alpha _ { \nu } = 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 .