Implications from simulated strong gravitational lensing systems:
  constraining cosmological parameters using Gaussian Processes
  Strongly gravitational lensing systems (SGL) encodes cosmology information in
source/lens distance ratios $\mathcal{D}_{\rm obs}=\mathcal{D}_{\rm
ls}/\mathcal{D}_{\rm s}$, which can be used to precisely constrain cosmological
parameters. In this paper, based on future measurements of 390 strong lensing
systems from the forthcoming LSST survey, we have successfully reconstructed
the distance ratio $\mathcal{D}_{\rm obs}$ (with the source redshift $z_s\sim
4.0$), directly from the data without assuming any parametric form. A recently
developed method based on model-independent reconstruction approach, Gaussian
Processes (GP) is used in our study of these strong lensing systems. Our
results show that independent measurement of the matter density parameter
($\Omega_m$) could be expected from such strong lensing statistics. More
specifically, one can expect $\Omega_m$ to be estimated at the precision of
$\Delta\Omega_m\sim0.015$ in the concordance $\Lambda$CDM model, which provides
comparable constraint on $\Omega_m$ with Planck 2015 results. In the framework
of the modified gravity theory (DGP), 390 detectable galactic lenses from
future LSST survey would lead to stringent fits of $\Delta\Omega_m\sim0.030$.
\textbf{Finally, we have discussed three possible sources of systematic errors
(sample incompleteness, the determination of length of lens redshift bin, and
the choice of lens redshift shells), and quantified their effects on the final
cosmological constraints. Our results strongly indicate that future strong
lensing surveys, with the accumulation of a larger and more accurate sample of
detectable galactic lenses, will considerably benefit from the methodology
described in this analysis. }
