Diffuse neutrino supernova background as a cosmological test

The future detection and measurement of the diffuse neutrino supernova background will shed light on the rate of supernovae events in the Universe, the star formation rate and the neutrino spectrum from each supernova. Little has been said about what those measurements will tell us about the expansion history of the universe. The purpose of this article is to show that the detection of the diffuse supernova neutrino background will be a complementary tool for the study and possible discrimination of cosmological models. In particular, we study three different cosmological models: the $\Lambda$ Cold Dark Matter model, the Logotropic universe and a bulk viscous matter-dominated universe. By fitting the free parameters of each model with the supernova Ia probe, we found that the predicted number of events computed with the best fit parameters for the $\Lambda$-Cold dark matter model and with the Logotropic model are the same, while a bulk viscous matter-dominated cosmological model predicts $\sim 3$ times more events. We show that the current limit set by Super-Kamiokande on the diffuse supernova neutrino background flux gives complementary constraints on the free parameters of a bulk viscous matter-dominated universe. Furthermore, this limit implies, within a $\Lambda$ Cold Dark Matter model, that the universe should be expanding with $H_0 > 21.5 ~\rm{Km/sec/Mpc}$ independently of the content of dark matter $\Omega_m$.