Probing Scalar-Induced First-Order Phase Transitions with the Diffuse Supernova Neutrino Background

We investigate the possibility of probing a scalar-induced first-order phase transition (FOPT) inside core-collapse supernovae through the diffuse supernova neutrino background (DSNB). We consider a light scalar coupled to neutrinos that is produced and thermalised in the proto-neutron-star core. This leads to two distinct neutrino components: a prompt contribution from thermally produced scalars and a delayed, spectrally narrow contribution from the decay of coherent scalar excitations due to the FOPT. We study the resulting DSNB signal at Super-Kamiokande, Hyper-Kamiokande, and DUNE, finding a strong dependence on the neutrino mass ordering. The recent Super-Kamiokande data already constrain the scalar parameter space for inverted ordering and quasi-degenerate neutrino masses, while future detectors can significantly improve this sensitivity. Our results demonstrate that DSNB measurements can provide a novel probe of finite-temperature scalar dynamics in core-collapse supernovae.