Dark Energy as a Violation of the Equivalence Principle

How much dark energy weights?

A. Füzfa and J.-M. Alimi

LUTh – Observatoire de Paris

A. Füzfa, J.-M. Alimi, Phys. Rev. D 73, 023520 (2006)

A. Füzfa, J.-M. Alimi, under preparation

Angular size of CMB anisotropies (WMAP):

Large-scale structures properties (baryon acoustic oscillation, galaxy counts, peculiar velocities, …) : m~0.3

What is the missing Dark Energy (DE)?

(X~0.7)

Effect on cosmic expansion : Hubble diagram of type Ia supernovae

Evidences in favour of dark energy

TOTh²

Flu

ctua

tions

(C

2l)

Angular size (°)

mh²

bh²

TOT~1.01m~0.3

Hubble diagram of type Ia supernovae

Type Ia Supernovae appear fainter than expected: Cosmic expansion has recently accelerated

or (and?) Supernovae are not standard candles at that time

What is the effect of dark energy?D

ista

nce

mod

uli

Old «  standard » cosmology TOT=m=1

Redshift

SNLS First year data set (2006)

Baryons~5%

Cold Dark Matter~25%

Radiations~0.01%

Dark Energy~70%

The « concordance » model :Dark energy is a positive cosmological constant

The cosmological constant problems

Cosmic acceleration : vacuum has non-vanishing energy =0 : space expands less gravitational energy less expansion >0 : space expands more vacuum energy more expansion

Quantum Theory : vacuum has a huge energy (uncertainty on ground state)

Observations:

Why is the cosmological constant that small?

Why is vacuum energy of the order of the critical energy today?

(is it really constant?)

pa

a3

2

p4764 10 GeVmPlth Total vacuum energy density:

Fine-tuning problem!

4470, 10 GeVc

obs

Coincidence problem!

3 if 0

pa Violation of the

strong energy condition

Is dark energy (DE) a gravitational rebel?

The equivalence principle:

What if dark energy ALONE violates the equivalence principle? Cosmic expansion is no more ruled by Friedmann laws in recent times Fundamental constants vary (GN, gauge coupling constants, …)

Impacts on cosmology:

All energies (including gravitational ones)

are equivalent for producing gravitation

Early universe (CMB, BBN) Luminosity curves of SNe Ia

Precision tests of General Relativity Observed Universality of free fall

OK if DE is a late process Modification of luminous

distance and GN

This DE should be TRANSIENT Too few DE on small scales

Why should gravitation couple universally to any kind of matter?

Cosmology without equivalence principle Tensor-scalar theories of gravitation (Dicke, Brans, Fierz, Jordan)

(universal coupling => Weak equivalence principle)

gASRgxdS mattermmatter24 , 2

2

1

031'1'''²3

2

m

pp

d

Ad

ap

mm

log and

)log(with

Cosmological

dynamics

Post-NewtonianConstraints

V

112

520

10

10

yrG

G

General Relativity(GR)

Cosmology with non-equivalent dark energy

Cosmic soup : ordinary matter (baryons, photons, ...) ruled by the weak equivalence principle + dark energy sector violating the equivalence

The universal coupling to matter Amatter() defines the observable metric

Violation of the weak equivalence principle:

Competitive cosmological dynamics

gAS

gASRgxdS

DEDEDE

mattermmatter

2

24

,

, 22

1

gAg m2~ taAta m ~~

DEmatter AA

tda

adtH ~~

~~~ 2~

~~~~a

aatq

02

32

3 mmDEDEDE pH

Repulsion term Attraction toward general relativity

Which candidate for non-equivalent DE? DE is a late process: pDE<pmatter~0

Transient mechanism : phase transition to positive pressures no need anymore to violate the strong energy condition p<-/3 Ideal candidate : new gauge interaction of Born-Infeld type

(renormalisation of point-like singularities, string theory, …)

1

~

16

1

2

11

2

84

4

FFFF

cc

cBIL

Low-energy limit:Yang-Mills dynamics

(radiation)High-energy limit:Vacuum polarization

(Nambu-Goto string gas)

4cBI

4cBI

4cBI

Phase transition2 aBI

3 aBI

4 aBI

Illustration of the mechanism1) Matter-dominated era : attraction toward GR

2) Born-Infeld gauge field domination: repulsion from GR3) Phase transition of the BI gauge interaction into radiation and attraction toward GR

1)

2)

3)

2)

3)

1)

2) 3)

Energy Density

Variation of G

Acceleration factor

The proof of the pudding :adequation to SNLS 1st year data

CDM : /dof=NEBI: dof

Combined effect of varying GN and cosmic

acceleration!

Data from P. Astier et al., A & A. 447 (2006)

The proof of the pudding :adequation to SNLS 1st year data

Dark Energy dominated Universe(as suggested by CMB, LSS)

Constraints on General Relativity OK!

The repulsing action of non-equivalent dark energy is not active today because of its radiative nature! (BI feature)

Conclusion : Is the violation of the equivalence principle a solution to

the cosmological constant problems? A completely new picture of dark energy :

Dark Energy does not « fall » in the same way as ordinary matter Deviation from GR during dark energy domination followed by a return to GR

provided by ordinary matter Good adequacy with Hubble diagrams (cosmic acceleration and variation of GN),

constraints on GR and physics in the radiative era Born-Infeld gauge interaction is an ideal candidate for non-equivalent dark

energy (late domination, quicker decoupling, no violation of the energy condition)

Perspectives: Post-recombination effect on CMB, effects on structure formation (GN(z)) Search for similar mechanisms for inflation and lightness of vacuum energy

4Pl

th m

447

0, 10 GeVc