The Backreaction Conjectureto explain Dark Energy

Thomas Buchert, CRALyon

MPIK May 26, 2014

The Standard Model

G = T

? a(t) δij 2 t

The Standard Model works ! Baryons

~ 5%

Radiation ~ 0.01%

Dark Energy~ 68 %

Dark Matter

~ 27%

Astier et al. 2006

The Standard Model does not work ! Baryons

~ 5%

Radiation ~ 0.01%

Dark Energy~ 68 %

Dark Matter ~

27%

fundamental scalar field / new particles ?

other laws of gravitation ?

effect of geometricalinhomogeneities ?

backreactionconjecture

Acceleration in the Standard Model

Λa(t) δij 2 t

local acceleration

global acceleration

apparent accelerationa(t) =V (t) ⅓

Generalizing the Standard Model

t

1/3aD= VR

Einstein Spacetime

4g = - dt2 + gij dXi dXj

gijt

a(t)

Averaging Einstein’s Equations

Spatial Average on a compact domain :

Restmass conservation on the domain D

Non - Commutativity

Acceleration Law :

Expansion Law :

Conservation Law :

Integrability :

Kinematical Backreaction

Effective Friedmann Equations

Effective Scalar Field :`Morphon´

Buchert, Larena, Alimi arXiv: gr-qc / 0606020

G = T

m +

Pm + P

m +

Pm + P

=

=

Volume Partitioning

Volume Partitioning

D

M

Volume Partitioning

D

M

D EM= υ

Structure formation and Dark Energy

Roukema, Ostrowski, Buchert arXiv: 1303.4444

Acceleration in the Multiscale Model

Q D

Acceleration in the Multiscale Model

Wiegand, Buchert arXiv: 1002.3912

Average is friedmannian for :

Locally isotropic models (homogeneous) Special LTB models with homogeneous curvature

Integral Properties of Relativistic Models

Average is non-friedmannian :

generic scaling solutions : n = p relativistic perturbation theory : n = p = -1

Unstable Sectors :

Q < 0 and <R> > 0

Q > 0 and <R> < 0

Averaged Cosmologies

Near FRW Cosmologies: Q small

Global Gravitational Instability

Roy, Buchert, Carloni, Obadia arXiv: 1103.1146

Buchert, Larena, Alimi arXiv: gr-qc / 0606020

Phase Space for = 0

Unstable Sectors = 0

DE

DM

Dark Energy Sector = 0

1/aD

Q > 0 and <R> < 0

1/aD

0

21

1/aD

<R>D - 2 ≈ – 6 HD2

QD ≈ 0 <> ≈ 0 :

Volume-dominance of Voids

Sloan Digital Sky Survey - slices

Todai, Tokyo 150000 galaxies

E u c l i d e a n

Observational Strategies

C

log(1+z)

Template Metrics

EuclidLarena, Alimi, Buchert, Kunz, Corasaniti arXiv: 0808.1161

structure formation changes the geometry of the average cosmology

Dark Energy and Dark Matter exist in terms of “curvature energies“ qualitative understanding of the mechanism is completed and it works in the right direction

quantitative understanding in terms of non-perturbative models is in progress reinterpretation of observations !

Conclusions

Further Reading :

arXiv:gr-qc/0001056

0707.21531103.20161112.5335