Probing Lorentz violation in neutrino propagation from a core-collapse supernova

Supernova explosions provide the most sensitive probes of neutrino propagation, such as the possibility that neutrino velocities might be affected by the foamy structure of space-time thought to be generated by quantum-gravitational effects. Recent two-dimensional simulations of the neutrino emissions from core-collapse supernovae suggest that they might exhibit variations in time on the scale of a few milliseconds. We analyze simulations of such neutrino emissions using a wavelet technique, and consider the limits that might be set on a linear or quadratic violation of Lorentz invariance in the group velocities of neutrinos of different energies, v/c=[1±(E/M_νLV1)] or [1±(E/M_νLV2)²], if variations on such short time scales were to be observed, where the mass scales M_νLVi might appear in models of quantum gravity. We find prospective sensitivities to M_νLV1~2×10¹³ GeV and M_νLV2~10⁶ GeV at the 95% confidence level, up to 2 orders of magnitude beyond estimates made using previous one-dimensional simulations of core-collapse supernovae. We also analyze the prospective sensitivities to scenarios in which the propagation times of neutrinos of fixed energies are subject to stochastic fluctuations.