Effect of axion-like particles on the spectrum of the extragalactic gamma-ray background

Axion-like particles (ALPs) provide a feasible explanation for the observed lower TeV opacity of the Universe. If the anomaly TeV transparency is caused by ALPs, then the fluxes of distant extragalactic sources will be enhanced at photon energies beyond TeV, resulting in an enhancement of the observed extragalactic gamma-ray background (EGB) spectrum. In this work, we have investigated the ALP modulation on the EGB spectrum at TeV energies. Our results show that in the most optimistic case, the existence of ALPs can cause the EGB spectrum to greatly deviate from the prediction of a pure extragalactic-background-light (EBL) absorption scenario. The deviation occurs at approximately $\gtrsim$1 TeV, and the current EGB measurements by Fermi-LAT cannot identify such an effect. We also find that most of the sensitive ALP parameters have been ruled out by existing constraints, leaving only a small region of unrestricted parameters that can be probed using the EGB effect investigated in this work. Observations from forthcoming very-high-energy instruments like LHAASO and CTA may be beneficial for the study of this effect.