Limits on the Isotropic Diffuse Flux of Ultrahigh Energy $\gamma$ Radiation

Diffuse ultrahigh energy $\gamma$ radiation can arise from a variety of astrophysical sources, including the interaction of ${10}^{20}\mathrm{eV}$ cosmic rays with the 2.7 K microwave background radiation or the collapse of topological defects created in the early Universe. We describe a sensitive search for diffuse $\gamma$ rays at ultrahigh energies using the Chicago Air Shower Array–Michigan Muon Array experiment. An isotropic flux of radiation is not detected, and we place stringent upper limits on the fraction of the $\gamma$-ray component relative to cosmic rays ( $<{10}^{-4\mathrm{}}$) at energies from $5.7\times {10}^{14}$ to $5.5\times {10}^{16}\mathrm{eV}$. This result represents the first comprehensive constraint on the $\gamma$-ray flux at these energies.