The strongest bounds on some forms of Lorentz and $CPT$ violation come from astrophysical data, and placing such bounds may require understanding and modeling distant sources of radiation. However, it is also desirable to have bounds that do not rely on these kinds of detailed models. Bounds that do not rely on any modeling of astrophysical objects may be derived both from laboratory experiments and certain kinds of astrophysical observations. The strongest such bounds on isotropic modifications of electron, positron, and photon dispersion relations of the form $E^2=p^2+m^2+ϵp^3$ come from data on cosmological birefringence, the absence of photon decay, and radiation from lepton beams. The bounds range in strength from the $4\times {10}^{-13}$ to $6\times {10}^{-33}(\mathrm{GeV}{)}^{-1}$ levels.

• Received 25 October 2010

DOI:https://doi.org/10.1103/PhysRevD.83.056012