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

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/λ. 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 (∝ 1/λ) and the Faraday term (∝ λ² ) yields a rotation measure RM = -6023 ± 228~rad~m⁻², with the Bayesian information criterion (BIC) showing no preference for the EEP term (Δ BIC = -1.15). Using the nominal value of the Galactic potential integral, the 95% statistical upper limit on the EEP amplitude gives |Δγₚ| < 2 × 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 γ-ray polarization bounds.