Can reverberation-measured quasars be used for cosmology?

Quasars have been proposed as a new class of standard candles analogous to Supernovae, as their large redshift range and high luminosities make them excellent candidates. Reverberation mapping (RM) method enables to estimate the distance to the source from the time delay measurement of the emission lines with respect to the continuum, since the time delay depends on the absolute luminosity of the source. This radius-luminosity (RL) relation exhibits a low scatter and it was thus proposed for cosmological purposes. However, in recent years the increase in the studied sample, and in particular the inclusion of highly accreting QSO has increased the dispersion in the RL relation, with many objects showing time delays shorter than the expected. Using H$\beta$ RM measurements for 117 sources with $0.002<z<0.9$ and $41.5<\mathrm{log}~L_{5100}<45.9$, we find a correction for the time delay based on the dimensionless accretion rate considering the virial factor anti-correlated with the FWHM of H$\beta$. This correction decreases the scattering in the accretion parameters compared with the typical value used, which is directly reflected by suppressing the RL relation dispersion. We also confirm the anti-correlation between the excess of variability and the accretion parameters. With this correction we are able to build the Hubble diagram and estimate the cosmological constants $\Omega_m$ and $\Omega_\Lambda$, which are consistent with the standard cosmological model at 2$\sigma$ confidence level. Therefore, RM results can be used to constrain cosmological models in the future.