First test of the Einstein equivalence principle with the radio polarization of a gamma-ray burst afterglow

Abstract The Einstein equivalence principle (EEP) requires identical Shapiro time delays for the two circular polarization eigenstates of light; any differential delay rotates the polarization angle of linearly polarized light by a term scaling as $1/\lambda$. We perform the first test of this effect with a gamma-ray burst (GRB) radio afterglow, using the quasi-simultaneous 9--25~GHz Karl G. Jansky Very Large Array (VLA) polarimetry of GRB~260310A at $z = 0.153$, whose single Faraday screen and single reverse-shock component suppress the astrophysical systematics of persistent sources. Fitting the polarization angle as a function of wavelength with the intrinsic angle, the EEP term ($\propto 1/\lambda$) and the Faraday term ($\propto \lambda^{2}$ ) yields a rotation measure ${\rm RM} = -6023 \pm 228$~rad~m$^{-2}$, with the Bayesian information criterion (BIC) showing no preference for the EEP term ($\Delta{\rm BIC} = -1.15$). \textbf{Using the nominal value of the Galactic potential integral, the 95\% statistical upper limit on the EEP amplitude gives $|\Delta\gamma_{p}| < 2 \times 10^{-19}$. The calibration uncertainty in the potential integral is not included in this limit and represents a separate systematic uncertainty.} This constrains the difference between the parametrized post-Newtonian parameters of the two circular states and is complementary to existing radio and $\gamma$-ray polarization bounds.