  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 $\Omega_m$.
