Supernova Neutrino Background Bound on the SFR History

The purpose of the present study is to compare the predictions of different models of star formation rate (SFR) history in the universe with the upper limit of Super Kamiokande for the neutrino background. To this aim we have calculated the expected neutrino density for the most popular models of SFR history, Hogg et al. ,Glazebrook et al., Cole et al., Yuksel et al., Hernquist et al. and Kaplinghat et al. Differerent from previous studies we have used the $\Lambda$CDM model with $\Omega_{\Lambda} = 0.7$. We have assumed that the detector used for the detection the neutrino flux is SuperK and also we have assumed that the electron neutrinos produced in the Supernovae oscillate equally to the three standard model flavors. By these assumptions all models stay below the upper limit of SuperK on the event rate and the detection of the supernova relic neutrino background (SRNB) remains undetected. Future neutrino detectors such as KM3Net will be able to detect the SRNB and distinguish between the models of the SFR history.