Propagation of Very-high-energy γ-Rays from Distant Blazars

We rederive the possible dependence of the redshift with a very-high-energy (VHE) γ -ray photon index. The results suggest that the universe to VHE γ -rays is becoming more transparent than expected. We introduce the extragalactic background light (EBL) and photon to axion-like particle (ALP) oscillations to explain this phenomenon. We concentrate our analysis on 70 blazars up to redshift z ≃ 1. Assuming this correlation is solely the result of photon-photon absorption of VHE photons with the EBL, with deviations between the predictions and observations, especially at redshifts 0.2 < z < 1. We then discuss the implications of photon-ALP oscillations for the VHE γ -ray spectra of blazars. Strong evidence shows that (1) the results of the EBL attenuation show that the VHE γ -ray photon index increases nonlinearly at the ranges of redshift 0.03 < z < 0.2 and (2) the photon-ALP oscillation results in an attractive characteristic in the VHE γ -ray photon index at the ranges of redshift 0.2 < z < 1. We suggest that both EBL absorption and photon-ALP oscillation can influence the propagation of VHE γ -rays from distant blazars.