Gamma-ray luminosity function of blazars and the cosmic gamma-ray background: Evidence for the luminosity-dependent density evolution

We present a comprehensive study of the gamma-ray luminosity function (GLF) of blazars and their contribution to the extragalactic diffuse gamma-ray background (EGRB). Radio and gamma-ray luminosity correlation is introduced with a modest dispersion, consistent with observations, to take into account the radio detectability, which is important for blazar identification. Previous studies considered only pure luminosity evolution (PLE) or pure density evolution, but here we introduce the luminosity-dependent density evolution (LDDE) model, which is favored on the basis of the evolution of the X-ray luminosity function (XLF) of AGNs. The model parameters are constrained by likelihood analyses of the observed redshift and gamma-ray flux distributions of the EGRET blazars. Interestingly, we find that the LDDE model gives a better fit to the observed distributions than the PLE model, indicating that the LDDE model is also appropriate for gamma-ray blazars and that the jet activity is universally correlated with the accretion history of AGNs. The normalization between the GLF and XLF is consistent with the unified picture of AGNs, when the beaming and a reasonable duty cycle of jet activity are taken into account. We then find that only 25% - 50% of the EGRB can be explained by unresolved blazars with the best-fit LDDE parameters. Unresolved blazars can account for all the EGRB only with a steeper index of the faint- end slope of the GLF, which is marginally consistent with the EGRET data but inconsistent with XLF data. Therefore, unresolved AGNs cannot be the dominant source of the EGRB, unless there is a new population of gamma-ray emitting-AGNs that evolves differently from the XLF of AGNs. Predictions for the GLAST mission are made, and we find that the best-fit LDDE model predicts about 3000 blazars in the entire sky, which is considerably fewer (by a factor of more than 3) than a previous estimate.