Strong Gravitation Lensing And Its Cosmic Constrains

Astronomical observations have demonstrated that our universe is undergoing an accel-erated expansion. All these data sets indicate that our universe is currently dominated by an energy component, dubbed as dark energy. What are the properties of the dark energy? To understand the nature of this dark side of our universe, one should use the information from the cosmic observations. Strong lensing has developed into an important astrophysical tool for probing both astrophysics and cosmology.In this dissertation, on the basis of the current observed data of strong lesning, several dark energy models are constrained. Specifically, the content of this paper can bo broadly di-vided into three chapters. In chapter1, the basic theory of strong lensing. In chapter2, dark energy cosmological model. In chapter3, based on X-ray observations, the velocity dispersion of the singular isothermal sphere model is different from the observed stellar velocity disper-sion, a free parameter that relates the velocity dispersion and the stellar velocity dispersion. Then the problem becomes to how to deal with the free parameter fE. It is crucial because it has an effect on result. We take the ratio of angular diameter distances from different lens system as cosmic observations Dijbos=θEiσ0i2/θEijσ0i2. Then one can constrain cosmological models. In the end, the conclusions and discussion are drawn.