Cosmological Tests with the FSRQ Gamma-ray Luminosity Function

The extensive catalog of $\gamma$-ray selected flat-spectrum radio quasars (FSRQs) produced by \emph{Fermi} during a four-year survey has generated considerable interest in determining their $\gamma$-ray luminosity function (GLF) and its evolution with cosmic time. In this paper, we introduce the novel idea of using this extensive database to test the differential volume expansion rate predicted by two specific models, the concordance $\Lambda$CDM and $R_{\rm h}=ct$ cosmologies. For this purpose, we use two well-studied formulations of the GLF, one based on pure luminosity evolution (PLE) and the other on a luminosity-dependent density evolution (LDDE). Using a Kolmogorov-Smirnov test on one-parameter cumulative distributions (in luminosity, redshift, photon index and source count), we confirm the results of earlier works showing that these data somewhat favour LDDE over PLE; we show that this is the case for both $\Lambda$CDM and $R_{\rm h}=ct$. Regardless of which GLF one chooses, however, we also show that model selection tools very strongly favour $R_{\rm h}=ct$ over $\Lambda$CDM. We suggest that such population studies, though featuring a strong evolution in redshift, may nonetheless be used as a valuable independent check of other model comparisons based solely on geometric considerations.