  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.
