Effect of VSR invariant Chern-Simon Lagrangian on photon polarization

We propose a generalization of the Chern-Simon (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term.