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We use 118 H$\beta$ quasar (QSO) observations in the redshift range $0.0023\leq z \leq 0.89$ to simultaneously constrain cosmological model parameters andQSO 2-parameter radius-luminosity ($R-L$) relation parameters in six differentcosmological models. We find that the $R-L$ relation parameters for these QSOsare independent of the assumed cosmology so these QSOs seem to bestandardizable through the $R-L$ relation (although there is a complicationthat might render this untrue). Cosmological constraints obtained using theseQSOs are weak, more favor currently decelerated cosmological expansion, andtypically are in $\sim 2\sigma$ tension with those obtained from a jointanalysis of baryon acoustic oscillation and Hubble parameter measurements.Extending the $R-L$ relation to a 3-parameter one to try to correct for theaccretion rate effect does not result in a reduction of the cosmologicalconstraints discrepancy nor does it result in the hoped-for significantreduction of the intrinsic scatter of the $R-L$ relation.

Do reverberation-measured H$\beta$ quasars provide a useful test of cosmology?