Dark Energy from Backreaction

1. Dark Energy from Backreaction Thomas Buchert LMU-ASC Munich, Germany & University of Bielefeld, Germany Collaborations : Mauro Carfora (Pavia, Italy): Averaging Riemannian Geometry Jürgen Ehlers (Golm, Germany): Averaging Newtonian Cosmologies George Ellis (Cape Town, South Africa): Averaging Strategies in G.R. Toshifumi Futamase (Sendai, Japan): Averaging and Observations Akio Hosoya (Tokyo, Japan): Averaging and Information Theory

2. I. The Standard Model II. Effective Einstein Equations Buchert: GRG 32, 105 (2000) : `Dust’ Buchert: GRG 33, 1381 (2001) : `Perfect Fluids’ III. Dark Energy from Backreaction Räsänen: astro-ph/ 0504005 (2005) Kolb, Matarrese & Riotto: astro-ph/ 0506534 (2005) Nambu & Tanimoto: gr-qc/ 0507057 (2005) Ishibashi & Wald: gr-qc/ 0509108 (2005) … …

3. The Cosmic Triangle The Standard Model Cosmological Parameters Bahcall et al. (1999)

4. The Concordance Model 0,3 0 0,7 Bahcall et al. (1999)

5. Simulations of Large Scale Structure E u c l i d e a n MPA Garching

6. Sloan Digital Sky Survey–Sample 12 • 150000 galaxies E u c l i d e a n Todai, Tokyo

7. II. Effective Einstein Equations Averaging the scalar parts Non-commutativity The role of information entropy The averaged equations The cosmic equation of state

8. The Idea Averaged Raychaudhuri Equation Averaged Hamiltonian Constraint

9. Generic Domains 1/3 aD= VR d2 s = - dt2 + gij dXi dXj t t a(t) Einstein Spacetime gij

10. Non-Commutativity

11. Relative Information Entropy Kullback-Leibler : S > 0 t S > 0 : Information in the Universe grows in competition with its expansion

13. The Hamiltonian Constraint Averaged Hamiltonian Constraint : < R > + < K2 – Kij Kji > = 16 G <  > + 2 Define : <  > = : 3 HD Define : Q = 2/3 < ( - <  >)2 > - 2 < 2> The Hamiltonian constraint : R + K2 – Kij Kji = 16 G  + 2 Decompose extrinsic curvature : -Ki J = 1/3 iJ + iJ

14. The averaged Hamiltonian Constraint Generalized Friedmann Equation

15. The Cosmic Quartet

16. The Cosmic Equation of State

17. Mean field description

18. Out-of-Equilibrium States

19. III. Dark Energy from Backreaction Kolb et al. 2005 :

20. Estimates in Newtonian Cosmology vanishes for periodic boundaries vanishes for spherical motion measures deviations from a sphere is negligible on large scales

21. Global Integral Properties of Newtonian Models Boundary conditions are periodic !

22. Result :spatial scale 100 Mpc/h

23. T h e r e f o r e … A classical explanation of Dark Energy through Backreaction is only conceivable in General Relativity !

24. Particular Exact Solutions I Buchert 2000

25. H o w e v e r … What happens, if the averaged curvature is coupled to backreaction ?

26. Particular Exact Solutions II Buchert 2005 ; Kolb et al. 2005

27. Global Stationarity 

28. Particular Exact Solutions III Globally Static Cosmos without  Buchert 2005

29. Particular Exact Solutions III Globally Static Cosmos without  Global Equation of State :

30. Particular Exact Solutions IV Globally Stationary Cosmos without  Buchert 2005

31. Particular Exact Solutions IV Globally Stationary Cosmos without  Global Equation of State :

32. Particular Exact Solutions V Averaged Tolman-Bondi Solution Nambu & Tanimoto 2005

33. Particular Exact Solutions VI Scaling Solutions Buchert, Larena, Alimi 2006

34. Cosmic Phase Diagram  = 0 Friedmann  = 0 Phantom quintessence q m

35. Evolution of Cosmological Parameters today 

36. C o n c l u s i o n s `Near-Friedmannian’ : no coupling between Q and <R> Standard Perturbation Theory : Q / V-2 <R>/ a-2 `Hard Scenario’ : strong coupling between Q and <R> Large backreaction out of `near-Friedmannian’ data `Soft Scenario’ : regional fluctuations of a global out-of-equilibrium state ( peff / -1/3 eff ) with strong initial expansion fluctuations