The high-redshift evolution of the GLF is uncer- tain, as there are no appropriate samples of gamma- ray blazars and X-ray AGNs above z = 3. Thus we constructed new GLFs by combining the U03 XLF with evolutionary constraints from the Sloan Digital Sky Survey (SDSS) quasar luminosity function data [53]. The SDSS quasar luminosity function is well constrained up to z ∼ 5. 

Fig. 5 shows the expected cumulative redshift distribution of blazars that are detectable by Fermi above 100 MeV. Two sets of curves are plotted corre- sponding to the one- and five-year survey sensitivity. Solid and dashed curves refer to the cases of whether or not the SDSS quasar constraint is taken into ac- count. Note that intergalactic absorption effects are not included here, as they are not expected to be im- portant below 1 GeV [50–52]. The results imply that Fermi may detect some blazars up to z ∼ 6 during the five-year survey. Measurements of the spectra of such blazars above 1 GeV through subsequent, deep obser- vations should provide interesting constraints on the high-z UV background. More details will be presented in a forthcoming publication. 

We have compared our prediction of the EGRB spectrum [26] with the recent Fermi data, and made quantitative predictions for the next four years of the Fermi mission. In Ref. [26], we constructed a model of the blazar gamma-ray luminosity function (GLF), taking into account the blazar SED sequence and the LDDE luminosity function inferred from X-ray obser- vations of AGNs. The GLF model parameters are constrained by fitting to the observed flux and red- shift distribution of the EGRET blazars. With this model, we can predict the EGRB spectrum in a non- trivial way, rather than assuming simple power-law spectra. 

The contribution from non-blazar AGNs to the EGRB is also considered, using the nonthermal coro- nal electron model [28]. This model gives a natu- ral explanation for the observed cosmic MeV back- ground, and we examined whether the X-ray to GeV gamma-ray background radiation can be accounted for by the two population model including blazars and non-blazar AGNs. 

Our predicted blazar EGRB spectrum matched very well with the latest Fermi EGRB data. This indicates that blazars are the dominant population of the EGRB and that other components such as dark matter annihilation do not contribute to EGRB signif- icantly. This also indicates that the use of blazar SED sequence was valid. The predicted spectrum including blazars and non-blazar AGNs is also in good agree- ment with the observed data from X-ray to 100 GeV. Therefore, blazars and non-blazar AGNs are likely the 

## VI. CONCLUSIONS 

primary sources of the cosmic X-ray and gamma-ray background radiation. Our model predicts that it is possible to account for 80 % of the observed EGRB flux above 100 MeV with the sum of the blazar and non-blazar AGN components, where blazars alone ac- count for about 45 %. The two components are com- parable at ∼ 100 MeV, with blazars and non-blazar AGNs dominating at higher and lower energies, re- spectively. 

From the viewpoint of the EGRB spectrum from MeV to GeV, we argue that the dominant component contributing to the MeV background is non-blazar AGNs that are also responsible also for the CXB, rather than MeV blazars as proposed by Ref. [29]. 

We predicted the flux distribution of blazars by our model, and we found that 750 and 1200 blazars in all sky should be detected by Fermi , assuming a sen- sitivity limit of F lim = 3 × 10 $_{−}$9 and 1 × 10 $_{−}$9 pho- tons cm $_{−}$2 s $_{−}$1 above 100 MeV corresponding to one and five year survey sensitivity. This number is sig- nificantly lower than the predictions by many of the previous studies. About 4–50 of non-blazar AGNs are expected to be detected by Fermi with 5-year sur- vey. Fermi should resolve almost all of the EGRB flux from blazars into discrete blazars, with percentages of > ∼ 98% with 5-year survey. On the other hand, less than 0.1% of the EGRB flux from non-blazar AGNs can be resolved into discrete sources. Therefore, we have a clear prediction: Fermi will resolve almost all of the EGRB flux into discrete sources at photon en- ergies > ∼ 1 GeV where blazars are dominant, while a significant fraction of the EGRB flux will remain un- resolved in the low energy band of < ∼ 100 MeV where non-blazar AGNs have a significant contribution. This prediction can easily be tested, only with the source counts and the EGRB estimates by Fermi data. 

We also made predictions for future detections of high-redshift blazars. Since the GLF is uncertain at z ≥ 3 due to lack of direct observational data, we con- strained the redshift evolution of our original AGN XLF using SDSS quasar data. With this assumption, we find that Fermi may find some blazars up to z ∼ 6 during the five year survey. Such high-redshift GeV blazars will offer a new probe of the formation histo- ries of early stars and galaxies via GeV spectral at- tenuation signatures caused by the high-redshift UV background radiation. 

This work was supported by the Grant-in-Aid for the Global COE Program ”The Next Generation of Physics, Spun from Universality and Emergence” and Scientific Research (19047003, 19047004, 19740099) from the Ministry of Education, Culture, Sports, Sci- ence and Technology (MEXT) of Japan. YI acknowl- 

## Acknowledgments 

