Tests of the Einstein Equivalence Principle using TeV Blazars

The observed time delays between different energy bands from TeV blazars provide a new interesting way of testing the Einstein Equivalence Principle (EEP). If the whole time delay is assumed to be dominated by the gravitational field of the Milky Way, the conservative upper limit on the EEP can be estimated. Here we show that the strict limits on the differences of the parameterized post-Newtonian parameter $\gamma$ values are $\gamma_{\rm TeV}-\gamma_{\rm keV}<3.86\times10^{-3}$ for Mrk 421 and $\gamma_{\rm TeV}-\gamma_{\rm keV}<4.43\times10^{-3}$ for Mrk 501, while expanding the scope of the tested EEP energy range out to the TeV--keV range for the first time. With the small time lag from the 0.2--0.8 TeV and $>0.8$ TeV light curves of PKS 2155-304, a much more severe constraint on $\gamma$ differences of $\sim10^{-6}$ can be achieved, although the energy difference is of order of $\sim$ TeV. Furthermore, we can combine these limits on the energy dependence of $\gamma$ with the bound on the absolute $\gamma$ value $\gamma-1\sim0.3\%$ from light deflection measurements at the optical (eV) bands, and conclude that this absolute bound on $\gamma$ can be extended from optical to TeV energies.