Cosmic Transients Test Einstein's Equivalence Principle out to GeV Energies

The Einstein Equivalence Principle (EEP) can be probed with astrophysical sources emitting simultaneously different types of neutral particles, or particles with varying energies, by testing their time of flight through the same gravitational field. Here we use the time delays between correlated photons from cosmological transients to constrain the accuracy of the EEP. We take data from two gamma-ray bursts as an example, and use, as a lower limit to the theoretical time delays between different energies, delays arising from only the gravitational field of our own galaxy. We then show that the parameterized post-Newtonian parameter $\gamma$ is the same for photons over energy ranges between eV and MeV and between MeV and GeV to a part in $10^{-7}$, which is at least one order of magnitude better than previous limits. Combining this bound on the wavelength dependence of $\gamma$ with the absolute bound $|\gamma-1|<0.3\%$ from light-deflection measurements at optical (eV) wavelengths, we thus extend this absolute bound on $\gamma$ to GeV energies.