$\gamma$-ray polarization constraints on Planck scale violations of special relativity

Using recent polarimetric observations of the Crab Nebula in the hard X-ray band by INTEGRAL, we show that the absence of vacuum birefringence effects constrains $O(E/M)$ Lorentz violation in QED to the level $|\xi |<9\times {10}^{-10}$ at $3\sigma$ CL, tightening by more than 3 orders of magnitude previous constraints. We show that planned X-ray polarimeters have the potential to probe $|\xi |\sim {10}^{-16}$ by detecting polarization in active galaxies at red-shift $\sim 1$.

Figure 1

Constraint for the polarization degree. Dependence of $\Pi$ on $\xi$ for the distance of the CN and photons in the 150–300 keV range, for a constant $\mathcal{P}(k)$.

Figure 2

Constraint for the polarization rotation case. Left panel: dependence of $\tan (2{\theta }_{\mathrm{f}})$ on $\xi$. The spikes correspond to rotations by $\pi /4$. Right panel: a zoom-in on the interesting range of values. The constraint is cast according to Eq. (6).

Figure 3

Expected constraints from medium X- and soft $\gamma$-ray polarimetry of extragalactic sources. High-energy scale $k_2=10\mathrm{keV}$ (left panel) and 1 MeV (right panel), with $\kappa \equiv k_1/k_2$ from 0.1 to 0.99. Points in the left panel refer to the characteristics of a new generation X-ray polarimeter [37] assuming that polarization is detected from the mentioned objects. The constraints are derived as in case of Eq. (4) for a concordance cosmology (${\Omega }_m=0.28$, ${\Omega }_{\Lambda }=0.72$ and $H_0=73\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$).