On Testing the Equivalence Principle with Extragalactic Bursts

An interesting test of Einstein's equivalence principle (EEP) relies on the observed lag in arrival times of photons emitted from extragalactic transient sources. Attributing the lag between photons of different energies to the gravitational potential of the Milky Way (MW), several authors derive new constraints on deviations from EEP. It is shown here that potential fluctuations from the large scale structure are at least two orders of magnitude larger than the gravitational potential of the MW. Combined with the larger distances, for sources at redshift $z\gtsim 0.5$ the {\it rms} of the contribution from these fluctuations exceeds the MW by more than 4 orders of magnitude. We provide actual constraints for several objects based on a statistical calculation of the large scale fluctuations in the standard $\Lambda$CDM cosmological model.