Stellar Initial Mass Function (IMF) Probed with Supernova Rates and Neutrino Background: Cosmic-average IMF Slope Is ≃2–3 Similar to the Salpeter IMF

The stellar initial mass function (IMF) is expressed by $\phi(m) \propto m^{-\alpha}$ with the slope $\alpha$, and known as poorly-constrained but very important in studies of star galaxy formation. There are no sensible observational constraints on IMF slopes beyond Milky Way nearby galaxies. Here we combine two sets results, 1) cosmic densities core-collapse supernova explosion (CCSNe) rates 2) far ultraviolet radiation (and infrared re-radiation) densities, which sensitive to massive ($\simeq 8-50 \,{\rm M}_\odot$) moderately 2.5-7 stars, respectively, constrain at $m>1\,{\rm M}_\odot$ a freedom redshift evolution. Although evolution identified uncertainties, find that average $z=0$ $\alpha=1.8-3.2$ 95 % confidence level comparable Salpeter IMF, $\alpha=2.35$, marks first constraint IMF. We show forecast for Nancy Grace Roman Space Telescope survey will provide significantly strong $\delta \alpha\simeq 0.5$ over $z=0-2$. Moreover, an independent probe instead 1), suggest use diffuse supernovae neutrino background (DSNB), relic neutrinos from CCSNe. expect Hyper-Kamiokande observations 20 years improve better than those obtained today, if systematic uncertainties DSNB production physics reduced future numerical simulations.