1. the Cosmological Constant Problem Roland TRIAY Centre de Physique Théorique CNRS Université de Provence Int. Journ. Mod. Phys. D 14,10,1667 (2005) Nonlinear Cosmological Workshop - NCP (2006) Nice

2. the Cosmological Constant Observations Geometrical Status Modeling Gravitational Structures “Einstein’s biggest blunder” Prelude

3. Observations - the 80th In the past : Dynamics of galaxies in clusters Minimum age of the Universe In the 80’s:Hubble diagram (QSOs, BCGs), VLSS (QSOs) (spatially) closed Universe

4. Observations - Nowadays Nowadays : CMB temperature fluctuations Hubble diagram (SuperNovæ)

5. Observations-SNa A.G. Riess etal astro-ph/0402512

6. Observations - Nowadays A.V Filippenko astro-ph/0410609

7. Face to the  -Problem « The Cosmological Constant From the Viewpoint of String Th. » E. Witten 2000 « The Cosmological Constant Problems » S. Weinberg 2000 « The Cosmological Constant » S. Carrol 2000 « The Case for a Positive Cosmological  -term » V. Sahni, A. Starobinsky 2000 « The Cosmological Constant and Dark Energy » P.J.E. Peebles, B. Ratra 2002 « On the Casimir Energy Contribution to the Obs. Value of … » I.O Cherednikov 2002 « The Cosmological Constant Problem » J. W. Moffat 2003 « Cosmological Constant Weight of the Vacuum » T. Padmanabham 2003 …

8. Status of   -  Geometry) The gravitational field and its sources are characterized by Schwarzschild solution - Newton approximation

9. Dimensional analysis of EE

10. Modeling gravitational structures With  : Gravitation becomes repulsive at “large” scale No  -effect in Solar neighborhood Small effect in the outerpart of the Galaxy Intervenes at the edge of LSC Homogeneity scale (Modified) Newton law

11. The cosmological Constant Problem The contribution of quantum fluctuations A similar problem happens when one assumes Solar neighborhood Primordial epoch ( Vacuum dominate expansion) Another version of the Cosmological Constant Problem

12. Understanding the acceleration of the cosmological expansion Rescaling !!! Understanding Quantum Gravity !!!