Abstract
The propagation of TeV gamma rays can be strongly modified by $B$-field induced conversion to axionlike particles (ALPs). We show that, at such high energies, photon dispersion is dominated by background photons---the only example where photon-photon dispersion is of practical relevance. We determine the refractive index for all energies and find that, for fixed energy density, background photons below the pair-production threshold dominate. The cosmic microwave background alone provides an ``effective photon mass'' of ${m}_{\ensuremath{\gamma}}^{2}=\ensuremath{-}(1.01\text{ }\text{ }\mathrm{neV}\ifmmode\times\else\texttimes\fi{}\ensuremath{\omega}/\mathrm{TeV}{)}^{2}$ for $\ensuremath{\omega}\ensuremath{\lesssim}1000\text{ }\text{ }\mathrm{TeV}$. The extragalactic background light is subdominant, but local radiation fields in the Galaxy or the source regions provide significant contributions. Photon-photon dispersion is small enough to leave typical scenarios of photon-ALP oscillations unscathed, but big enough to worry about it case by case.
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