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 $\mathcal{D}^{obs}_{ij}=\theta_{\mathrm{E_{\mathrm{i}}}}\sigma_{\mathrm{0_{\mathrm{j}}}}^2/\theta_{\mathrm{E_{\mathrm{j}}}}\sigma_{\mathrm{0_{\mathrm{i}}}}^2$ as cosmic observations, one can {\it completely} eliminate the uncertainty caused by the relation $\sigma_{\mathrm{SIS}}=f_{\mathrm{E}}\sigma_0$ 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 $\Lambda$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.