Speed Variations of Cosmic Photons and Neutrinos from Loop Quantum Gravity

Recently a series of analyses on the flight time of cosmic photons and neutrinos suggests that the speed of light \emph{in vacuo} takes the energy-dependent form $v(E)\simeq 1-E\mathrm{/}{E}_{\text{LIV}}^{\gamma }$ with $E_{\text{LIV}}^{\gamma }\approx 3.6\times {10}^{17}\text{ GeV}$, and meanwhile the speed of neutrinos is proposed to be $v(E)\simeq 1\pm E\mathrm{/}{E}_{\text{LIV}}^{\nu }$ with $E_{\text{LIV}}^{\nu }\approx 6.5\times {10}^{17}\text{ GeV}$ and $\pm$ representing the helicity dependence. This novel picture immediately urges us to provide a satisfactory theoretical explanation. Among all the attempts to predict the speed variations from quantum gravity, we find that loop quantum gravity can serve as a good candidate for explaining the aforementioned picture consistently.