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, $v/c=[1\pm (E/M_{\nu \mathrm{LV}1})]$ or $[1\pm (E/M_{\nu \mathrm{LV}2}{)}^2]$, if variations on such short time scales were to be observed, where the mass scales $M_{\nu \mathrm{LVi}}$ might appear in models of quantum gravity. We find prospective sensitivities to $M_{\nu \mathrm{LV}1}\sim 2\times {10}^{13}\mathrm{GeV}$ and $M_{\nu \mathrm{LV}2}\sim {10}^6\mathrm{GeV}$ 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.

• Received 7 November 2011

DOI:https://doi.org/10.1103/PhysRevD.85.045032