# Precision Test of the Weak Equivalence Principle from Gamma-Ray Burst Polarization

## TL;DR

This paper uses gamma-ray burst polarization data to test the weak equivalence principle, deriving extremely tight constraints on possible violations by analyzing polarization rotation effects.

## Contribution

It provides the most stringent limits to date on WEP violation by analyzing gamma-ray burst polarization, surpassing previous bounds by at least six orders of magnitude.

## Key findings

- More than 60% polarization can be preserved despite large polarization rotation angles.
- Constraints on WEP violation parameter Δγ are as low as 1.3×10⁻³³ and 0.8×10⁻³³ from GRB data.
- Harder spectra and wider energy range polarization measurements improve WEP tests.

## Abstract

If the weak equivalence principle (WEP) is broken, the measured values of the parametrized post-Newtonian parameter $\gamma$ from photons with left- and right-handed circular polarizations should differ slightly, leading to the arrival-time difference of these two circular components. Thus, the polarization vector of a linearly polarized light may rotate during the propagation. The rotation angle of the polarization vector depends on both the photon energy and the distance of the source. It is believed that if the rotation angle differs by more than $\pi/2$ over an energy range, then the net polarization of the signal would be significantly suppressed and could not be as high as the observed level. Thus, the detection of highly polarized photons implies that the relative rotation angle ($\Delta\Theta$) should not be too large. In this paper, we give a detailed calculation on the evolution of gamma-ray burst (GRB) polarization arising from a possible violation of the WEP, and we find that more than $60\%$ of the initial polarization degree can be conserved even if $\Delta\Theta$ is larger than $\pi/2$. In addition, to tightly constrain the WEP violation, GRBs with harder spectra and polarization observations in a wider energy range seem to be favored. Applying our formulas to the measurements of linear polarization from GRB 110721A and GRB 061122, we obtain strict limits on the differences of the $\gamma$ values as low as $\Delta\gamma<1.3\times10^{-33}$ and $\Delta\gamma<0.8\times10^{-33}$. These provide the most stringent limits to date on a deviation from the WEP, improving at least 6 orders of magnitude over previous bounds.