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

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

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

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

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

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

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

The Idea Averaged Raychaudhuri Equation Averaged Hamiltonian Constraint

Generic Domains t 1/3 a D = V R Einstein Spacetime Einstein Spacetime d 2 s = - dt 2 + g ij dX i dX j g ij t a(t)

Non-CommutativityNon-Commutativity

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

The Hamiltonian constraint : R + K 2 – K i j K j i = 16  G  + 2  Decompose extrinsic curvature : -K i J = 1/3   i J +  i J Averaged Hamiltonian Constraint : + = 16  G + 2  Define : = : 3 H D Define : Q = 2/3 ) 2 > - 2 The Hamiltonian Constraint The Hamiltonian Constraint

The averaged Hamiltonian Constraint The averaged Hamiltonian Constraint Generalized Friedmann Equation

The Cosmic Quartet The Cosmic Quartet

The Cosmic Equation of State The Cosmic Equation of State

Mean field description

Out-of-Equilibrium States

III. Dark Energy from Backreaction Kolb et al :

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

Global Integral Properties of Newtonian Models Boundary conditions are periodic !

Result : spatial scale 100 Mpc/h

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

Particular Exact Solutions I Buchert 2000

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

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

Global Stationarity  

Particular Exact Solutions III Globally Static Cosmos without  Buchert 2005

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

Particular Exact Solutions IV Globally Stationary Cosmos without  Buchert 2005

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

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

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

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

Evolution of Cosmological Parameters today 

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