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 technique. In low-redshift quasars, the combination of RM 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.