Supernova-Neutrino-Boosted Dark Matter from All Galaxies

It has been recently proposed that the boosted dark matter (BDM) by supernova neutrinos (SN$\nu$) from SN1987a or from the next Galactic supernova (SN) can serve as a novel component to probe nonvanishing interaction between dark matter (DM) and the standard model leptons [Y.-H. Lin et al., Phys. Rev. Lett 130, 111002 (2023) and Y.-H. Lin et al., Phys. Rev. D 108, 083013 (2023)]. In this Letter, we extend this concept and evaluate the present-day diffuse flux of SN$\nu$ BDM originated from all galaxies at higher redshifts. We show that by considering this diffuse BDM (DBDM) component, the best sensitivity on the product of the energy-independent DM-$\nu$ and DM-electron cross sections, $\sqrt{\sigma_{\chi\nu}\sigma_{\chi e}}\simeq \mathcal{O}(10^{-37})$ cm$^2$ for sub-MeV DM, can be obtained with large-size neutrino experiments such as Super-Kamiokande or Hyper-Kamiokande, surpassing the estimated SN$\nu$ BDM bound from SN1987a. We also examine the impact due to the presence of DM spikes around the supermassive black holes in galaxies on SN$\nu$ BDM and DBDM. Our results suggest that both the DBDM and the SN$\nu$ BDM probes are robust to the uncertain properties of DM spikes, unless the next Galactic SN happens to occur at a location extremely close to or right behind the Galactic Center along the SN line of sight.