Standardizing reverberation-mapped H$\beta$ active galactic nuclei using time-averaged radius$-$luminosity relations with 5100\,Å\,, broad H$\beta$, and narrow \OIII\ luminosities

Active galactic nuclei (AGN) have been studied as alternate probes in cosmology due to their large and stable luminosities and broad redshift range. Previously it was shown that higher-redshift AGN that were reverberation-mapped (RM) using broad Mg,$\text{textsc}ii$ and C,$\text{textsc}iv$ lines are standardizable and yield weak cosmological constraints that are consistent with those from better-established probes. In contrast, lower-redshift AGN that were reverberation-mapped using the broad H$\beta$ line exhibited tensions with the standard cosmological model, in particular they preferred currently decelerating cosmological expansion. Here we study the standardizability of a homogeneous RM H$\beta$ sample of $\sim 100$ AGN (over redshifts $0.00308\le z\le 0.8429$), whose H$\beta$ time delays and three luminosity tracers (at 5100,Å,, broad H$\beta$, and narrow [O,$\text{textsc}iii$]) are averaged over several epochs. We find that this averaged sample is standardizable using three $R-L$ relations. While for luminosities corresponding to 5100,Å, and the broad H$\beta$ line the cosmological constraints prefer currently decelerating cosmological expansion, the cosmological parameters for the narrow [O,$\text{textsc}iii$] luminosity are more consistent with those from better-established probes and they are in agreement with currently accelerating cosmological expansion. This demonstrates for the first time that narrow-line region [O,$\text{textsc}iii$] can be utilized for AGN standardization and cosmological constraints. Selecting proper photoionizing flux proxies for the broad-line region is thus crucial in studies of RM AGN standardizability.