Dark Energy from Structure Formation

1
Dark Energy from Structure Formation
Thomas Buchert
LMU-ASC Munich, Germany
SFB 375 Abschlussworkshop Gaißach, Bad
Tölz 2006
2
SFB 375 / B3 Highlights
I. Minkowski Valuations
II. SDSS Minkowski Functional Project
III. Analytical Models incl. velocity
dispersion deviations from
mean-field gravity Lagrangian perturbation
theory and models for the
non-perturbative regime. Relativistic
generalization (M. Ostermann).
IV. The Averaging Problem in Relativistic
Cosmology Effective Einstein equations
Backreaction issues
Backreaction as common origin of Dark Energy and
Dark Matter.
3
V. Dark Energy from Structure Formation
Buchert GRG 32, 105 (2000) Effective
Einstein Equations
Räsänen astro-ph/
0504005 (2005) Kolb, Matarrese Riotto
astro-ph/ 0506534 (2005) Nambu Tanimoto
gr-qc/ 0507057 (2005) Ishibashi Wald
gr-qc/ 0509108 (2005)
Ellis Buchert gr-qc/0506106
(2005) Räsänen astro-ph/0607626 (2006)
4
The Standard Model
The Cosmic Triangle
Cosmological Parameters
Bahcall et al. (1999)
5
The Concordance Model
0,3 0 0,7
Bahcall et al. (1999)
6
Guidelines
Averaged Cosmologies
Near FRW Cosmologies Q small
Unstable Sector Q gt 0 ltRgt
lt 0
Newtonian Simulations Q 0
Averaged Ricci curvature evolves different from
constant curvature
Curvature-Fluctuation coupling
7
Non-Commutativity
8
Relative Information Entropy
Kullback-Leibler
S gt 0 ?t S gt 0 Information in the Universe
grows in competition with its expansion
9
The Idea
Averaged Raychaudhuri Equation
Averaged Hamiltonian Constraint
10
Generic Domains
1/3
aD VR
d2 s - dt2 gij dXi dXj
t
t
a(t)
Einstein Spacetime
gij
11
(No Transcript)
12
Dark Energy from Backreaction
Kolb et al. 2005
13
Boundary conditions are periodic !
14
Curvature-Fluctuation-Coupling
15
Mean field description
16
Out-of-Equilibrium States
17
Particular Exact Solutions I Buchert 2000
18
Particular Exact Solutions IV Globally Stationary
Cosmos without ? Buchert 2005
19
Particular Exact Solutions V Averaged
Tolman-Bondi Solution
Nambu Tanimoto 2005
20
Particular Exact Solutions VI Scaling Solutions
Buchert, Larena, Alimi 2006
21
Particular Exact Solutions VI Scalar Field and
its Potential
Buchert, Larena, Alimi 2006
22
Cosmic Phase Diagram ? 0
Friedmann ? 0
Phantom quintessence
q
?m
23
Dark Energy equation of state
w? p?/?? const.
?Dk ¼ 0
?D?
?DR
?DQ
24
Evolution of Cosmological Parameters
today
??
25
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
26
Further Reading
Reviews
astro-ph / 0607626
Räsänen 2006 Ellis Buchert 2005

gr-qc / 0506106
Equations and Solutions
gr-qc / 0509124
Buchert 2005
Scalar Field Correspondence
gr-qc / 0606020
Buchert, Larena, Alimi 2006