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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 $\mathcal{D}^{obs}_{ij}=θ_{\mathrm{E_{\mathrm{i}}}}σ_{\mathrm{0_{\mathrm{j}}}}^2/θ_{\mathrm{E_{\mathrm{j}}}}σ_{\mathrm{0_{\mathrm{i}}}}^2$ as cosmic observations, one can {\it completely} eliminate the uncertainty caused by the relation $σ_{\mathrm{SIS}}=f_{\mathrm{E}}σ_0$ which characterizes the relation between the stellar velocity dispersion $σ_0$ and the velocity dispersion $σ_{SIS}$. Via our method, a relative tight constraint to the cosmological model space can be obtained, for the spatially flat $Λ$CDM model as an example $Ω_m=0.143_{- 0.143-0.143-0.143}^{+ 0.000769+0.143+0.489}$ in $3σ$ regions. And by using this method, one can also probe the nature of dark energy and the spatial curvature of our Universe.