A New Gravitational Lens Phenomena by Cluster of Galaxies and the Measurement of Cosmological Constant

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This study investigates methods to determine the cosmological parameters, particularly cosmological constant using gravitational lensing. The following are results of the study.1. The distribution of angular separation between images of lensed quasar can be used to put the upper bound for the cosmological constant. We examined the magnification bias which plays an important role in this study and obtained more accurate estimation for this. Our result shows that the existence of the cosmological constant cannot be denied by the presently available observations.2. The number of giant luminous arcs in clusters of galaxies is unexpectedly large. We examined this problem and found that the presence of the cosmological constant increase the expected number of arcs.3. We showed that the observation of Einstein rings using large telescope such as SUBARU may impose a severe constraint on the cosmological constant.4. We studied the method to estimate the mass distribution of cluster of galaxies using weak shear field created by coherent distortion of background galaxies and applied the method to Q0957+561 and PG1115+080 to obtain the constraint on the Hubble parameter.