Lecture form Spring School on Strings, Cosmology and Particles (SSSCP2009), March 31-4 2009, Belgrade/Nis, Serbia

1. PREDRAG JOVANOVI Ć AND LUKA Č. POPOVI Ć ASTRONOMICAL OBSERVATORY BELGRADE, SERBIA Gravitational Lensing Statistics and Cosmology

5. Wilkinson Microwave Anisotropy Probe (WMAP) The "angular spectrum" of the fluctuations in the WMAP full-sky map, showing the relative brightness of the "spots" in the map vs. the size of the spots. The shape of this curve contain a wealth of information about the history of the universe

8. Content of the Universe

9. Gravitational lensing

10. Einstein Ring Radius of a gravitational lens

11. Examples: QSO 2237+030 ( z= 1.695), also known as “Einstein cross” and lensing galaxy ZW2237+030 ( z= 0.0394) RXJ1131-1231 PG 1115+080

13. Weak lensing: detection of dark matter unlensed lensed

14. Distribution of dark matter

15. The Hubble constant from gravitational lens time delays Kochanek & Schechter, 2003, astro-ph/0306040

16. Courbin, 2003, astro-ph/0304497 HST Key Project : determination of the H 0 by the systematic observations of Cepheid variable stars in several galaxies using HST

18. Likelihood contours at the 68%, 90%, 95%, and 99% confidence levels. The dotted line marks spatially flat cosmologies The separation distribution of the 12 CLASS lenses Mitchell et al. 2005, ApJ , 622, 81 Differential (thick) and cumulative (thin) probability along the line of spatially flat cosmologies

21. The ratio of lensed to total number of quasars and optical depth for three different flat cosmological models as a function of quasar redshift

22. Optical depth of cosmologically distributed gravitational microlenses (Zakharov, Popovi ć and Jovanovi ć , 2004, A&A , 881)

23. Optical depth of cosmologically distributed gravitational microlenses for three different values of  L