Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Background Based on Fermi-LAT Observations

The Fermi-LAT has accumulated a large sample of blazars with known flux and spectral index. However, since blazars with harder spectra can be detected to lower fluxes than ones with softer ones with the LAT, the observed bi-variate flux-index distribution is severely truncated at low fluxes and softer spectra. Previously we have used the non-parametric method developed by Efron and Petrosian (EP) to correct the Fermi data for this truncation and obtained the true mono-variate distributions of spectral index and flux (commonly called the logN-logS relation) from which we obtained the blazar contribution to EGB as a function of flux directly from the data (Singal et al. 2012). Extrapolating this to lowest possible fluxes we estimated the total contribution of blazars to the EGB. By now many of the FSRQ blazars are identified with active galactic nuclei and their redshifts measured or obtained from archives (M. Shaw et al., 2012). With the addition of the redshifts we can now calculate the FSRQ blazar luminosities and from the tri-variate luminosity-index-redshift distribution determine the luminosity function and index distribution and their evolutions with redshifts. The EP method can be generalized to this three dimensional case (as we done for SDSS quasars; Singal et al. 2013). In this talk we will present the results from this analysis, which will allow us to compare the density and luminosity evolution of FSRQ blazars with other AGNs. In addition, we can determine the redshift and luminosity (instead of flux) variation of the contribution to the EGB which may allow a more reliable estimate of the total contribution of FSRQ blazars to the EGB.