Strong Gravitational Lensing and Its Cosmic Constraints

In this paper, we propose a new method to use the strong lensing data sets to constrain a cosmological model. By taking the ratio ${\mathcal{D}}_{ij}^{obs}={\theta }_{{\mathrm{E}}_{\mathrm{i}}}{\sigma }_{0_{\mathrm{j}}}^2\mathrm{/}{\theta }_{{\mathrm{E}}_{\mathrm{j}}}{\sigma }_{0_{\mathrm{i}}}^2$ as cosmic observations, one can {\it completely} eliminate the uncertainty caused by the relation ${\sigma }_{\mathrm{S}\mathrm{I}\mathrm{S}}=f_{\mathrm{E}}{\sigma }_0$ which characterizes the relation between the stellar velocity dispersion ${\sigma }_0$ and the velocity dispersion ${\sigma }_{SIS}$. Via our method, a relative tight constraint to the cosmological model space can be obtained, for the spatially flat $\mathrm{\Lambda }$CDM model as an example $\Omega_m=0.143_{- 0.143-0.143-0.143}^{+ 0.000769+0.143+0.489}$in$3\sigma$ regions. And by using this method, one can also probe the nature of dark energy and the spatial curvature of our Universe.