Do reverberation-measured Hβ quasars provide a useful test of cosmology?

We use 118 Hβ quasar (QSO) observations in the redshift range 0.0023 ≤ z ≤ 0.89 to simultaneously constrain cosmological model parameters and QSO 2-parameter radius-luminosity (R-L) relation parameters in six different cosmological models. We find that the R-L relation parameters for these QSOs are independent of the assumed cosmology so these QSOs seem to be standardizable through the R-L relation (although there is a complication that might render this untrue). Cosmological constraints obtained using these QSOs are weak, more favour currently decelerated cosmological expansion, and typically are in ~2σ tension with those obtained from a joint analysis of baryon acoustic oscillation and Hubble parameter measurements. Extending the R-L relation to a 3-parameter one to try to correct for the accretion rate effect does not result in a reduction of the cosmological constraints discrepancy nor does it result in the hoped-for significant reduction of the intrinsic scatter of the R-L relation.