  In the near future, new surveys promise a significant increase in the number
of quasars (QSO) at large redshifts. This will help to constrain the dark
energy models using quasars. The Large Synoptic Survey Telescope (LSST) will
cover over 10 million QSO in six photometric bands during its 10-year run. QSO
will be monitored and subsequently analyzed using the photometric reverberation
mapping (RM) technique. In low-redshift quasars, the combination of
reverberation-mapped and spectroscopic results have provided important
progress. However, there are still some facts which have to be taken into
account for future results. It has been found that super-Eddington sources show
time delays shorter than the expected from the well-known Radius-Luminosity
($R\mathrm{_{H\beta}}-L_{5100}$) relation. Using a sample of 117 H$\beta$
reverberation-mapped AGN with $0.02<z<0.9$, we propose a correction by the
accretion rate effect recovering the classical $R\mathrm{_{H\beta}}-L_{5100}$
relation. We determined the cosmological constants, which are in agreement with
$\Lambda$-Cold Dark Matter model within 2$\sigma$ confidence level, which is
still not suitable for testing possible departures from the standard model.
Upcoming LSST data will decrease the uncertainties in the dark energy
determination using reverberation-mapped sources, particularly at high
redshifts. We show the first steps in the modeling of the expected light curves
for H$\beta$ and MgII.
