Bounds on Parity Violation In the Cosmological Redshift
  Parity (P) violation in gravity would be a sure sign of new physics. We examine the possibility of P violation in the cosmological redshift. If right- and left-circularly polarized photons experience the redshift differently, the radiation from distant sources would tend to be depolarized, since the polarizations states would accumulate different phases during propagation. The resulting birefringence has an unusual signature--depending on z^2--quite unlike what is seen in other theories, including those with violation of local boost invariance. The observed broad-spectrum polarization of $\gamma$-ray bursts constrains the fractional difference between the right- and left-handed redshifts at the 6 x 10^(-37) level. 
Brett Altschul and Matthew Mewes
astro-ph.CO hep-ph