Dark Energy from Backreaction

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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
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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)
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The Standard Model
The Cosmic Triangle
Cosmological Parameters
Bahcall et al. (1999)
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The Concordance Model
0,3 0 0,7
Bahcall et al. (1999)
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Simulations of Large Scale Structure
E u c l i d e a n
MPA Garching
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Sloan Digital Sky SurveySample 12
E u c l i d e a n
Todai, Tokyo
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II. Effective Einstein Equations
Averaging the scalar parts Non-commutativity The
role of information entropy The averaged
equations The cosmic equation of state
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The Idea
Averaged Raychaudhuri Equation
Averaged Hamiltonian Constraint
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Generic Domains
1/3
aD VR
d2 s - dt2 gij dXi dXj
t
t
a(t)
Einstein Spacetime
gij
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Non-Commutativity
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Relative Information Entropy
Kullback-Leibler
S gt 0 ?t S gt 0 Information in the Universe
grows in competition with its expansion
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The Hamiltonian constraint R K2 Kij
Kji 16? G ? 2? Decompose extrinsic
curvature -Ki J 1/3 ? ?iJ ?iJ
Averaged Hamiltonian Constraint lt R gt lt
K2 Kij Kji gt 16? G lt ? gt 2? Define
lt ? gt 3 HD Define Q 2/3 lt
(? - lt ? gt)2 gt - 2 lt ?2 gt
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Generalized Friedmann Equation
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Mean field description
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Out-of-Equilibrium States
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III. Dark Energy from Backreaction
Kolb et al. 2005
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Estimates in Newtonian Cosmology
vanishes for periodic boundaries
vanishes for spherical motion
measures deviations from a sphere
is negligible on large scales
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Boundary conditions are periodic !
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Result spatial scale 100 Mpc/h
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T h e r e f o r e
A classical explanation of Dark Energy through
Backreaction is only conceivable
in General Relativity !
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Particular Exact Solutions I Buchert 2000
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H o w e v e r
What happens, if the averaged curvature is
coupled to backreaction ?
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Particular Exact Solutions II Buchert 2005
Kolb et al. 2005
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Global Stationarity
?
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Particular Exact Solutions III Globally Static
Cosmos without ? Buchert 2005
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Particular Exact Solutions III Globally Static
Cosmos without ?
Global Equation of State
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Particular Exact Solutions IV Globally Stationary
Cosmos without ? Buchert 2005
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Particular Exact Solutions IV Globally Stationary
Cosmos without ?
Global Equation of State
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Particular Exact Solutions V Averaged
Tolman-Bondi Solution
Nambu Tanimoto 2005
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Particular Exact Solutions VI Scaling Solutions
Buchert, Larena, Alimi 2006
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Cosmic Phase Diagram ? 0
Friedmann ? 0
Phantom quintessence
q
?m
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Evolution of Cosmological Parameters
today
??
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C o n c l u s i o n s
Near-Friedmannian no coupling between Q and
ltRgt Standard Perturbation Theory Q / V-2
ltRgt / a-2 Hard Scenario strong coupling
between Q and ltRgt Large backreaction out of
near-Friedmannian data Soft Scenario
regional fluctuations of a global out-of-equilibri
um state ( peff / -1/3 ?eff ) with strong initial
expansion fluctuations