Dark Energy and the AWEDark Energy and the AWE … Energy and the AWEDark Energy and the AWE*...

Dark Energy and the AWEDark Energy and the AWE** hypothesishypothesisDark Energy and the AWEDark Energy and the AWE hypothesishypothesis

JeanJean--Michel Alimi, André FüzfaMichel Alimi, André FüzfaJeanJean Michel Alimi, André FüzfaMichel Alimi, André FüzfaLaboratoire Univers et Theories, Laboratoire Univers et Theories,

Observatoire de ParisObservatoire de Paris

Miami 2007

S i 2007 b itt d Ph R D75 123007 (2007) t h/0702478 Ph R D 73 023520 (2006)Science 2007 submitted, Phys Rev D75, 123007 (2007),astro-ph/0702478 , Phys. Rev. D 73, 023520 (2006), gr-qc/0511090, Phys. Rev. Lett. 97, 061301 (2006), astro-ph/0604517,, SF2A 2006, MG11, FQTC Warrenton 2006, …* AWE means also Abnormally Weighting Energy

One of the most Chalenging problems in PhysicsOne of the most Chalenging problems in Physics

Several cosmological observations demonstrated that theSeveral cosmological observations demonstrated that the expansion of the universe is accelerating

What is causing this acceleration ?

H l b hi l i h D kHow can we learn more about this acceleration, the Dark Energy it implies, and the questions it raises ?

The Dark Energy asks the fundamental principles of our cosmological paradigm

OutlineOutline

Fundamental Principles in Cosmology.

Observational Evidences of Dark Energy.

Nature of Dark Energy.Theoretical Interpretations:

DE as a new exotic energy component or as a violation of a (Strong) CosmologicalDE as a new exotic energy component or as a violation of a (Strong) Cosmological Principle or as an extension of GR.

An « Iceberg » of Physical Theories behind the Dark Energy

The AWE hypothesis. Toward an unification of DM and DE problems.

A natural « dual GR » at cosmological scalesWhy the concordance model appears correct ?A natural phantom dark energyAWE dark matter as a time-dependent inertial massRemarkable observational predictionsRemarkable observational predictions

Gravitation - Microphysics

Fundamental Principles in CosmologyFundamental Principles in Cosmology

The Principle of General Covariance: Generalization from Galileo to Einstein

The Equivalence Principle: Universality of the free-fall (Minertial = Mgravitational) (10-inertial gravitational

12).Einstein’s General Relativity does not distinguish these two principles

• WEP: weak equivalence principle: Test bodies fall with the same acceleration independently of internal structure or compositionindependently of internal structure or composition • SEP: Strong equivalence principle: Test bodies fall with the same acceleration independently of gravitational binding energy.

μνμνμνμνπ TGgRgR 4

821

=Λ−−

Einstein’s General Relativity is the standard model of gravitation

μνμνμνμν cgg 42

Usually, the Cosmological Principle: Homogeneous and isotropic Universe• From theoretical point of view, it means the dynamics of the Universe is given only by a(t)

⎤⎡ 2d•FLRW: ⎥

⎦

⎤⎢⎣

⎡++

−−=

222222

2222 sin

1)( φθθ drdr

krdrtadtds

Supernovae type Ia

Observational Evidences of Dark EnergyObservational Evidences of Dark EnergySupernovae type Ia

Standard candlesTheir intrinsic luminosity is know, their apparent luminosity can be precisely measured (P.S.Corasaniti 2006)

The ratio of the two can provide the luminosity-distance (dL) of the supernova, the red shift z can be e at o o t e two ca p ov de t e u os ty d sta ce (dL) o t e supe ova, t e ed s t ca bemeasured independently from spectroscopy

Finally, one can obtain dL (z) or equivalently the magnitude(z) and draw a Hubble diagram

Type Ia Supernovae appear fainter than expected:yp p pp pCosmic expansion has recently accelerated or (and?) Supernovae are not standard candles at that time

─ HST Gold Sample─ 1st year SNLS collaborationm

odul

i m

-M

1st year SNLS collaboration─ « Old » Cosmology (SCDM, Ωm=1)─ Matter + DE (LCDM, Ωm=0.24 ; ΩL=0.76)

Riess et al ApJ 607 665 (2004)

Dis

tanc

e m

Riess et al., ApJ, 607, 665 (2004)P. Astier et al., A&A 447 (2006)

Redshift

Observational Evidences of Dark EnergyObservational Evidences of Dark Energy

CMB is an almost isotropic relic radiation of T=2.725±0.002 K CMB i t ill f th Bi B l

Evidence from Cosmic Microwave Background Radiation (CMB)

CMB is a strong pillar of the Big Bang cosmologyIt is a powerful tool to use in order to constrain several cosmological parameters

Ωmh²

uatio

ns (C

2 l)

Ωbh²

Fluc

tu b

ΩTOTh²

Geometry: Flat Universe (ΩT~1) , Present Energy Content: Matter : ~24% with Baryons: ~4%=> Dark Matter : ~ 20 % , => Missing Dark Energy: ~76%!


Numerous observational evidences: BAO, LSS, WL …Baryonic Acoustic Oscillations

n fu

nctio

n ─ SDSS Luminous Red Galaxies─ ΛCDM, ΩM=0.24 ; ΩΛ=0.76─ OCDM, ΩM=0.24

nt c

orre

latio

n OCDM, ΩM 0.24

Distance r (h-1 Mpc)

2-po

in

sta ce ( pc)

• Large-Scale distribution of galaxies (Power Spectrum)2dFGRS : 0.65<ΩΛ<0.85 (95% C.L.), SDSS: ΩM=0.24±0.02 (95% C.L.)

Counting clusters of galaxies can infer the matter energy density in the universe, ΩM ~0.3

(3/9)


The Concordance Model ΛCDMB 5%

Cosmic complementarityBaryons ~ 5%

CDM ~ 25%

Radiations ~ 0.01%

Dark Energy ~ 70%

Dark Matter ?Dark Matter ? Dark Energy ?Dark Energy ?

Nature of Dark Energy ?Nature of Dark Energy ?

Cosmological ParadigmCovariance PrincipleE i l P i i l

Gak

aa

38

2

2

=+⎟⎠⎞

⎜⎝⎛ ρπ&

}Equivalence PrincipleComological Principle

( )PGaa 3

34

+−= ρπ&&

New energy-component (ρ) Extensions to GR !!

}The Hypothesis

+ to LM and DM: Violation of the strong

energy conditionGeometrical

and Dynamical Interpretationρ

“Einstein’s General Relativity is the standard model of gravitation” is

conserved

3 if 0 ρ

−<> pa&& Extensions to GR can be interpreted as an extra

energy-component Standard Model and

The Cosmological Principle is discussed *

in a « quasi » Friedmann model ?

All proposed models of dark energy can be interpreted

and theoretical extensions

New vision of the Universe.

All proposed models of dark energy can be interpreted as an extra energy-component in a “quasi” Friedmann model

•Reinterpreting dark energy through backreaction: the minimally coupled morphon field, T. Buchert, J. Larena, AJM: CQG. 23, 6379 (2006), gr-qc/0606020, astro-ph/0609315, astro-ph/0612774

Nature of Dark Energy in Perspective? Nature of Dark Energy in Perspective? The Dark Cosmology IcebergThe Dark Cosmology Iceberg

The simple cosmological constant can be seen as the top of the iceberg of a deeper intriguing theory of gravitation

Cosmological Constant

gravitation

In the framework of Quintessence, Λ corresponds to the limiting case where the scalar field freezes in a non

Quintessence … N Ph i ?

{ }∫ Λ+−= RgxdSEinstein4

21κ

limiting case where the scalar field freezes in a non-vanishing energy state.

(SEP+WEP)Quintessence itself can be seen as the limiting case of

New Physics ?

Extra dimensions ( ){ }∫ +∂∂−−= ϕϕϕκ

μμ V 2

21 4 RgxdSgrav

Quintessence itself can be seen as the limiting case of Tensor-scalar gravity with negligible violation of Strong Equivalence Principle (SEP)

(NO SEP WEP)

Coupled dark energyChameleon… [ ] ( )[ ]μνμν ϕψϕ gASgSS mattermmattergrav

2,, += (NO SEP, WEP)Finally, there is a generalization of the non-minimal

couplings that embed the previous TST: the case where the non-minimal couplings are not universal.AWE hypothesis

[ ] ( )[ ]∑ ASSS 2

(NO SEP, NO WEP)This will constitutes the starting point of the

Abnormally Weighting Energy (AWE) Hypothesis.

[ ] ( )[ ]∑+=imatter

iiigrav gASgSS

2,, μνμν ϕψϕ

The AWE Hypothesis: The AWE Hypothesis: Cosmology without Equivalence PrincipleCosmology without Equivalence Principle

Tensor-scalar theories of gravitation* (universal coupling => NO SEP, WEP)

Dicke Jordan Frame (Observational Frame) Einstein Frame ( ) μνμν ϕ *~ 2 gAg M=

( ) [ ]μννμμνω gSgRgxdS MM

~,~~21 4 Ψ+

⎭⎬⎫

⎩⎨⎧ Φ∂Φ∂

ΦΦ

−Φ−= ∫ { } ( )[ ]μνμ

μ ϕψϕϕκ

*, 2*21 24 gASRgxdS MMM+∂∂−−= ∫

2 ⎞⎛⎞⎛⎞⎛ pp

Dicke-Jordan Frame (Observational Frame) Einstein Frame ( ) μνμν ϕ gg M

( ) ( ) 031'1'''²32 =⎟

⎠⎞⎜

⎝⎛ −+⎟

⎠⎞⎜

⎝⎛ −+⎟

⎠⎞⎜

⎝⎛

− ϕαρϕρϕϕ Mpp

( )λ

λ

Adal

)log( where

dd'with

∝

≡

Cosmological dynamics

( ) ( ) ϕϕαϕ dV ∫=

( ) ( )ϕ

ϕϕαdAd M

Mlog and =

Post-Newtonian Constraints

( )

( )4

20

520

20

1061

1021

21

−

−

×<=−

×<+

=−

d ααβ

ααγ

GR

ϕ ( )112

200

106

10612

1

−−×<

×<+

=

yrGG

d&

αϕβ

*Jordan 1949, Fierz 1956, Brans & Dicke 1961

The AWE Hypothesis: The AWE Hypothesis: The equivalence principleThe equivalence principle

The Equivalence Principle: all kinds of energies couple in the same way to gravitation

Weak equivalence principle (WEP): non-gravitational energiesWeak equivalence principle (WEP): non-gravitational energiesStrong equivalence principle (SEP): gravitational binding energy

Eff ti th i f it tiEffective theories of gravitation: Tensor Scalar gravity, low-energy limit of string theory *

{ }∫ ∂∂−−= ϕϕ μμ21 4 RgxdSgrav { }∫ ϕϕ

κ μ2ggrav

( )[ ] ( )[ ] ...,, 22 ++= μνμν ϕψϕψ gASgASS fermionsfermionsfermionsgaugegaugegaugematter

Ψi: matter field, Ai(ϕ) coupling functions, ϕ « dilaton »,Ψi: matter field, Ai(ϕ) coupling functions, ϕ « dilaton »,

Effective metric felt by energy i (« observable » frame for i) ( ) μνμν ϕ gAg i2~ =

Gravitation: spin 2 (gμν)+ spin 0 (ϕ) : NO SEP !p (gμν) p (ϕ)Non-universal coupling (Agauge(ϕ) ≠Afermions(ϕ), etc.) : NO WEP ⇒ NO SEP !

* Gasperini 2007, Damour & Polyakov 1994

The AWE HypothesisThe AWE Hypothesis

(In Einstein Frame) Energy content of the Universe is divided in 3 partsA gravitational sector described by pure spin 2 (graviton) and spin 0 (dilaton) degrees of freedom and a matter sector containing : The ordinary matter (baryons, photons, ...), ruled g y ( y , p , ),by the equivalence principle, defines the observable frame

AWE i l i h k i l i i l

{ } ( )[ ] ( )[ ]μνμνμ

μ ϕψϕψϕϕκ

*, *, 2*21 224 gASgASRgxdS AWEAWEAWEMMM ++∂∂−−= ∫

AWE sector violating the weak equivalence principle

( ) ( )ϕϕ AWEM AA ≠(In Dicke-Jordan Observable Frame) mixed degrees-of-freedom

The ordinary matter (baryons, photons, ...), ruled by the equivalence principle, defines the observable frame and follow geodesics of metric not of pure spin-2Invisible (AWE) sector has varying mass

[ ] ( )[ ]μνμννμ ϕψψω μν gMSgSgRgxdS AWEAWEMM~, ~, ~)(~~~

21 24 ++

⎭⎬⎫

⎩⎨⎧ Φ∂Φ∂

ΦΦ

−Φ−= ∫

( ) μνμν ϕ gAg M2~ = ( ) ( ) ( ) ( ) ( ) 2~

~~~~ , ~~

~1~~ , ~~a

aatqtdad

atHtaAta m &&&=== ϕ

2 ⎭⎩ Φ

The AWE Hypothesis: cosmological modelsThe AWE Hypothesis: cosmological models

{ } ( )[ ] ( )[ ]μνμνμ

μ ϕψϕψϕϕκ

*,*, 2*21 224 gASgASRgxdS AWEAWEAWEMMM ++∂∂−−= ∫

Einstein Frame

κ2The Action of the AWE Hypothesis generalizes the models DM-DE couplings Das, Corasaniti, Khoury 2006:Chameleon, Khoury, Weltman, Brax,Davis, van de Bruck 2004:However the AWE Hypothesis consider the scalar field is massless

1)(,)()( === ϕϕϕ βϕMDMAWE AeAA

ϕβϕβ ϕϕ MAWE eAeA MAWE == )(,)(

( ) ( )336

832 ,

38

3 *****2

*

***

*22

*

*2* +++−−=++=⎟⎟

⎠

⎞⎜⎜⎝

⎛= AWEAWEMMAWEM ppG

aaG

aaH ρρπϕρρπϕ

&&&&&

FLRW

( )( ) ( )( ) 034343 *******

* =−+−++ AWEAWEAWEMMM pGpGaa ρϕαπρϕαπϕϕ &&

&&

Let us consider that the AWE sector is l fl id d f th tt d i t d f th i

( ) ,,,*

*

*,

* *3aa

AWEMAWEMAWEMAWEM ρϕϕαρρ =+∇ &&

&

a pressureless fluid and focus on the matter-dominated era of the universe

Conservation equations !

( ) 3,

,,

*

**

aC

A

a

AWEMAWEMAWEM ϕρ =

3−∝ aBIρ

Dark Energy as a relaxation of the Weak Equivalence Principle Dark Energy as a relaxation of the Weak Equivalence Principle on Cosmological Scales.on Cosmological Scales.

( ) ( ) ( ) ( )ϕ M AACΑ

Α* **

The previous two fluids system can be rewritten as one field system

( ) ( ) ( ) ( )ϕϕϕϕρρρ AWEMM

AWEMT AAa

+=Α=+= ,*

* 3

( ) ( )We deduce

( ) ( ) ( ) ( ) ( )( )( )

*log' ,

1

))((( , 0''''²3

2

*

* add

dLogd

AWE

M

MAWEM ≡

+

−+=

Α=ℵ=+ℵ+

−ϕρ

ϕρϕαϕαϕα

ϕϕϕϕϕϕ

ϕ

, which corresponds to no violation of the WEP and/or if

( )AWE ϕρTST in matter-dominated era are easily retrived if ( ) ( ) ( )ϕϕαϕα ℵ== AWEM

AWEM ** ρρ >>

The present TST exibits a sophisticated convergence mechanism even in the case of very p p g ysimple constitutive coupling functions

( )( )

( )( )=ϕρ

ϕρϕ

ϕ

AWE

M

AWE

Mi A

AR ( ) ( )

( ) ( ) ( )( ) ( ) 0 , 0 =+=ℵ ∞

∞

∞∞∞ ϕα

ϕϕϕαϕ

ϕρϕ

AWEAWE

MiM

AWEAWE

AAR

Dark Energy as a relaxation of the Weak Equivalence Dark Energy as a relaxation of the Weak Equivalence Principle on Cosmological Scales.Principle on Cosmological Scales.

GR-like attractorsGR

at CMBe

pote

ntia

l1<<AWEb ρρ

ϕ

Effe

ctiv

e

1>>AWEb ρρ

Chameleon like Effect (Kh & W lt 2004 M t & Sh 2006 B t l 2004 M t & B

ϕ (Gravitational coupling)

Chameleon-like Effect (Khoury & Weltman 2004; Mota & Shaw 2006; Brax et al. 2004; Mota & Barrow 2004).

Relaxation of Weak Equivalence Principle on cosmological scales:Restricted WEP on isible matter ( normall eighting sector):

1<<DMb ρρ1>>ρρRestricted WEP on visible matter (« normally weighting » sector):

One space-time but two couplings GM and GAWE (« minimal » WEP violation) corresponding to different minima in the couplings functions

1>>DMb ρρ

Dark Energy as a relaxation of the Weak Equivalence Principle at Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales:cosmological scales: Toward an unification to DM and DEToward an unification to DM and DE

For any set of constitutive coulings functions, AM(ϕ), AAWE(ϕ), the resulting couling function A has at least one extremum and there exists a finite value of the effective

i i l li hi h i diff f GR( )G~gravitational coupling constant which is different from GR.( )ϕcG

ϕϕαϕϕαϕϕ

kkkk

AWEAWEMM

MA

== )( , )(22

( )

( ) ( )( )ϕϕ

ϕϕϕ

AdLog

k avec keC

CeA MA

k

M

AWEk MA

=ℵ

<+= 0, 22

( )ϕ

ϕd

=ℵ

The attracting value ϕ depends on the ratio of usual matter over abnormally weighting dustThe attracting value ϕ∞ depends on the ratio of usual matter over abnormally weighting dust and is intermediate between the value of ϕ for which AM(ϕ) extremum (when ρ*M>>ρAWE*) and the value of ϕ for which AAWE(ϕ) is extremum (when ρM*<<ρAWE*).

Dark Energy as a relaxation of the Weak Equivalence Principle at Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales:cosmological scales: Astrophysical discussionAstrophysical discussion

The violation of the WEP strongly depends on the ratio of usual matter energy density over AWE.

As both usual matter and AWE clusters, this violation is different with the scale considered.

Furthermore, the AWE is assumed to be dark and its gravitational collapse will be therefore quite different due to the abscence of the dissipative processes that allows usual matter like baryons to cluster so much compared to DM at low scales.

The domination of usual matter over AWE DM at small scales, which is a consequence of the different physical processes to which baryons are submitted will tend to make the WEP well verified at small scales.

The usual convergence mechanism toward GR with G* (Grav. Cst bare value) as an asymptotic value of the gravitational coupling constant is acting on scales where AWE DM is sub-dominant, i.e. at low scales.

W th f j t th t GR i ifi d th ll ( b l ti ) l t hi h thWe therefore conjecture that GR is verified on the very small (sub-galactic) scales at which the solar system or binary pulsar system constraints on GR have been established.

We then interprete the Hubble diagram of far-away supernovae only in terms of cosmic l ti ith t ti d t th i ti f th it ti l t t f tacceleration without corrections due to the variation of the gravitational constant for compact,

gravitationally bound objects. The precise computation of the deviations from GR with the scale would require a complexe

study of the structure formation in this AWE model.


( ) ( )McM GAGgAg μνμν ϕϕ *~ , *~ 22 ==Observational Frame

~~8 G

( ) ( ) AWEM

AWEMM

M TATTAT μνν

μμνν

μ ϕϕ *~ , *~ 44 −− ==

A (quasi) Friedman description

( ) ( )( )

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛ +++×+=

+== −

2

222

1

'3'631'1~~

3

~8~

'1*~~~

ϕααϕρρπ

ϕϕαϕ

MMAWEM

c

MM

GH

HAaaH&

( ) ( )2

22

2,

,

'631'~~~

~3

~8~

ϕααϕ

ρπ

ϕ++

Ω+Ω=Ω

=Ω

MMAWEM

AWEMcAWEM H

G

( ) ⎟⎠

⎜⎝ − 2'33 ϕ

ρρ AWEM ( ) 2'3 ϕϕ −AWEM

Accelating Universe in the AWE Hypothesis

FLRW-like but DM not scaling in a-3 (varying mass), and Exotic DE tracking DM and baryons

Accelating Universe in the AWE Hypothesis

( )

( )

MM

AWEMc

ddG

tdad

aα

ϕαϕ

ϕϕρρπ

~

232'

'3'21~~

3

~4~~

~1

22

2

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠

⎞⎜⎝

⎛ −−

−×+−=

( )AWEAWEMMMcG ραρααπ ~~~4 +−

Acceleration occurs in the observational frame, for instance, if αAWE<0 and ρAWE>>ρM


Type Ia supernovae Hubble diagram (Astier et al 2006)Ri=0.11, R∞=0.31, ΩM

0=0.04, ΩAWE0=0.26, t0(Gyr)=15,9, χ2/dof=1.03

( ) ( )zdMmz L~log5~

10=−=μ

ΛCDM

AWE

Blue: data from SLNS Usual Matter ≡ BaryonBlue: data from SLNSRed: data from HST Gold sample

Usual Matter ≡ BaryonAWE ≡ DM

⇒GM(ϕ) ≡ DE


Type Ia supernovae Hubble diagram (HST + SNLS data)

Usual Matter ≡ BaryonAWE ≡ DM

⇒2σ

⇒GM(ϕ) ≡ DE

1σ

1σ 03.0010

06.002.0

21.0

05.0+

+−

=Ω

=Ω

DM

b

2σ 01.021.0 −ΩDM

Measurement of baryons and DM distribution from SNe Ia alone!Independent predictions close to that of ΛCDM with a very good agreement

with BBN and CMB

Dark Energy as a relaxation of the Weak Equivalence Principle at Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: A natural phantom universecosmological scales: A natural phantom universe

An acelerating Universe in the AWE hypothesis

( )cGH ρρπ ~~~8~ 2 += ( )

( )effDEc

Tc

DET

GGd

ad

H

ωρπρπ

ρρ

31~3

~4~3

~4~~

~1

3

2

2

+−−=

+=

( )effDETtdaρρ

33~~ 2

Dark Energy as a relaxation of the Weak Equivalence Principle at Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: A unified description of DM and DEcosmological scales: A unified description of DM and DE

Constraints from SNe Ia Hubble diagrams

3σ 13σ

3σ

1σ

1σ

HST Gold DATA SNLS DATA

Λ ruled out 1σ, 2σ (HST) !ΩM in agreement with independant analysis !

Dark Energy as a relaxation of the Weak Equivalence Principle at Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: A natural phantom universecosmological scales: A natural phantom universe

Constraints from SNe Ia Hubble diagrams

2σ

1σ

2σ

1σ


ΩB ΩB


A natural phantom universe (super acceleration) !ΩB very good agreement with BBN and CMB analysises

The AWE HypothesisThe AWE Hypothesis

R d i D k E tR d i D k E tReducing Dark Energy toReducing Dark Energy toa new property of Dark Matter:a new property of Dark Matter:

The Anomalous GravityThe Anomalous Gravity

Open Question:Open Question:Open Question:Open Question:Test of the equivalence principle on cosmological scales ?Test of the equivalence principle on cosmological scales ?

How discriminating between all Dark Energy Models ? How discriminating between all Dark Energy Models ? IImplications on Structure Formationmplications on Structure Formation

AWE Dark Matter as a time-dependent inertial mass

( ) ( )( )

ϕϕ AWE

AAm ∝*

( ) ( )( )ϕ

ϕϕM

AWE

AAm ∝~

S F iStructure Formation. GN(t)Poisson Equation is modifiedInertiel Mass(t)Inertiel Mass(t)Free Fall Equation is modifiedObservational Frame

A Keystone Between Microphysics and Gravitation ?

The most remarkable feature of our model is that, besides of its cosmological predictions, it allows us to deduce a new constraint

To obtain the cosmological evolution described above, it is enough that

relating microphysics and gravitation:

the matter and AWE coupling functions have to be inversely proportional:

∞−∝ RAA )()( ϕϕWhere is the ratio at which ordinaty matter and DM

densities freeze once the scalar field reaches the attractor ϕ

∝ AweM AA )()( ϕϕ)( +∞→⎟

⎠⎞⎜

⎝⎛=∞ tR

DM

bρ

ρ

densities freeze once the scalar field reaches the attractor ϕ∞

From the cosmological data on supernovae, we find a R∞ close to unity ( t 68 % fid l l)(at 68 % confidence level)

)(38.1 , )(26.1 38.186.0

95.068.0 SNLSRHSTR +

−∞+−∞ ==

A Keystone Between Microphysics and Gravitation ?

We deduce an intriguing relation between the constant mass of baryons mb

and the changing DM mDM and gravitational strenght Gc

where the bar means the Earth laboratory value.

DMbNDMbc mmGxmmxG ××=×× )()( μμ

Although this relation does not fix the bare mass of DM, it rules its scaling by imposing a conservation of the product of the gravitational charges of baryons p g p g g yand DM. This phenomenological law, directly deduced from cosmological data

and linking together gravitational scales and masses of baryons and invisible matter glimpes at the intimate nature of gravitation.

The deep meaning of this relation constitutes a crucial question for theThe deep meaning of this relation constitutes a crucial question for the fundamental approaches that aim to unify gravity and microphysics with

explicit space-time dependancies of masses and couplings.

Dark Energy and the AWEDark Energy and the AWE** hypothesishypothesisDark Energy and the AWEDark Energy and the AWE hypothesishypothesis

JJ Mi h l Ali i A d é Fü fMi h l Ali i A d é Fü fJeanJean--Michel Alimi, André FüzfaMichel Alimi, André FüzfaThank you for your attention…Thank you for your attention…

* AWE means also Abnormally Weighting Energy

−40

−44

10−42

10−40

V4 )

BaryonsDMRadiationDEΛ

10−48

10−46

10−44

y de

nsiti

es (

GeV

4

10−52

10−50

10−48

Ene

rgy

10−2

10−1

100

10−52

Scale Factor a

Dark Energy and the AWEDark Energy and the AWE … Energy and the AWEDark Energy and the AWE*...

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