Dark Energy nd and the WE* AWE hypothesis Jean-Michel Alimi, André üzfa Füzfa Laboratoire Univers et Theories, Observatoire de Paris Miami 2007 also

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1 Dark Energy and the * hypothesis Jean-ichel Alimi, André Füzfa Laboratoire Univers et Theories, Observatoire de Paris iami 007 S i 007 b itt d Ph R D (007) t h/ Ph R D (006) Science 007 submitted, Phys Rev D75, (007),astro-ph/070478, Phys. Rev. D 73, 0350 (006), gr-qc/ , Phys. Rev. Lett. 97, (006), astro-ph/ ,, SFA 006, G11, FQTC Warrenton 006, * means also Abnormally Weighting Energy

2 One of the most Chalenging problems in Physics Several cosmological observations demonstrated that the expansion of the universe is accelerating What is causing this acceleration? How 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

3 Outline 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) Cosmological Principle or as an extension of GR. An «Iceberg» of Physical Theories behind the Dark Energy The hypothesis. Toward an unification of D and DE problems. A natural «dual GR» at cosmological scales Why the concordance model appears correct? A natural phantom dark energy dark matter as a time-dependent inertial mass Remarkable observational predictions Gravitation - icrophysics

4 Fundamental Principles in Cosmology The Principle of General Covariance: Generalization from Galileo to Einstein The Equivalence Principle: Universality of the free-fall ( inertial gravitational) (10-1 ). 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 composition SEP: Strong equivalence principle: Test bodies fall with the same acceleration independently of gravitational binding energy. 1 8πG R μν g μν R Λ g μν 4 T μν c Einstein s General Relativity is the standard model of gravitation 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) FLRW: ds dt dr a( t) + r dθ + r sin θ dφ 1 kr

5 Supernovae type Ia Observational Evidences of Dark Energy Standard candles Their intrinsic luminosity is know, their apparent luminosity can be precisely measured (P.S.Corasaniti 006) The ratio of the twocan provide dethe luminosity-distance dsta ce(d L ) of the supernova, the red shift z can be measured independently from spectroscopy Finally, one can obtain d L (z) or equivalently the magnitude(z) and draw a Hubble diagram Type Ia Supernovae appear fainter than expected: Cosmic expansion has recently accelerated or (and?) Supernovae are not standard candles at that time Distance moduli m- Riess et al., ApJ, 607, 665 (004) P. Astier et al., A&A 447 (006) HST Gold Sample 1st year SNLS collaboration «Old» Cosmology (SCD, Ω m 1) atter + DE (LCD, Ω m 0.4 ; Ω L 0.76) Redshift

6 Observational Evidences of Dark Energy Evidence from Cosmic icrowave Background Radiation (CB) CB is an almost isotropic relic radiation of T.75±0.00 K CB is a strong pillar of the Big Bang cosmology It is a powerful tool to use in order to constrain several cosmological parameters Ω m h² Fluctu uations (C l) Ω b h² b Ω TOT h² Geometry: Flat Universe (Ω T 1), Present Energy Content: atter : 4% with Baryons: 4% > Dark atter : 0 %, > issing Dark Energy: 76%!

7 Observational Evidences of Dark Energy Numerous observational evidences: BAO, LSS, WL Baryonic Acoustic Oscillations -poin nt correlation function SDSS Luminous Red Galaxies ΛCD, Ω 0.4 ; Ω Λ 0.76 OCD, Ω 0.4 Distance r (h -1 pc) Large-Scale distribution of galaxies (Power Spectrum) dfgrs : 0.65<Ω Λ <0.85 (95% C.L.), SDSS: Ω 0.4±0.0 (95% C.L.) Counting clusters of galaxies can infer the matter energy density in the universe, Ω 0.3 (3/9)

8 Observational Evidences of Dark Energy Cosmic complementarity The Concordance odel ΛCD Baryons 5% CD 5% Radiations 0.01% Dark Energy 70% Dark atter? Dark Energy?

9 Nature of Dark Energy? Cosmological Paradigm Covariance Principle Equivalence Principle i Comological Principle } a& k 8πGρ + a a 3 a&& 4πG ( ρ + 3P) a 3 New energy-component (ρ) The Hypothesis Extensions to GR!! + to L and D: Violation of the strong energy condition ρ a& & > 0 if p < 3 Standard odel and theoretical extensions Einstein s General Relativity is the standard model of gravitation is conserved The Cosmological Principle is discussed * New vision of the Universe. Geometrical and Dynamical Interpretation Extensions to GR can be interpreted as an extra energy-component in a «quasi» Friedmann model? 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, AJ: CQG. 3, 6379 (006), gr-qc/060600, astro-ph/ , astro-ph/061774

10 Cosmological Constant New Physics? Nature of Dark Energy in Perspective? The Dark Cosmology Iceberg Quintessence Extra dimensions Coupled dark energy The simple cosmological constant can be seen as the top of the iceberg of a deeper intriguing theory of gravitation 1 4 S Einstein d x g{ R + Λ} κ In the framework of Quintessence, Λ corresponds to the limiting case where the scalar field freezes in a nonvanishing energy state. 1 4 { } μ S grav d x g R μ + V( ) κ Quintessence itself can be seen as the limiting case of Tensor-scalar gravity with negligible violation of Strong Equivalence Principle (SEP) [ g ] Chameleon S S [ g, ] + S ψ, A ( ) hypothesis grav μν matter m matter μν (SEP+WEP) (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. S S grav [ g ] [ gμν ] + Si ψ i, Ai ( ), μν matter i (NO SEP, NO WEP) This will constitutes the starting point of the Abnormally Weighting Energy () Hypothesis.

11 The Hypothesis: Cosmology without Equivalence Principle Tensor-scalar theories of gravitation* (universal coupling > NO SEP, WEP) gμν A g * Dicke-Jordan Frame (Observational Frame) Einstein Frame μν ( ) μν S 1 ω( ) μν d 4 x g Φ R g Φ Φ Φ + S Ψ g 1 4 μ S d x g *{ R } + S ψ, A ( ) with ' d dλ where λ log(a) d log A and ( ) d Φ Cosmological dynamics ( ) μ ν [, ] μν κ μ [ g * ] '' 1 ' 1 3 ( 3 '²) + p + p ρ ρ V ( ) ( ) d ( ) 0 μν GR *Jordan 1949, Fierz 1956, Brans & Dicke 1961 Post-Newtonian Constraints γ 1 d β 1 d 0 ( 1+ ) ( ) 0 G& < 6 10 G 1 < 10 0 yr 5 <

12 The Hypothesis: The equivalence principle The Equivalence Principle: all kinds of energies couple in the same way to gravitation Weak equivalence principle (WEP): non-gravitational energies Strong equivalence principle (SEP): gravitational binding energy Effective theories of gravitation: ti Tensor Scalar gravity, low-energy limit of string theory * 1 4 S μ grav d x g { R μ } κ S ψ, A ( ) g S matter [ ] [ ( ) ] + S ψ, A g +... gauge gauge gauge μν fermions fermions fermions μν Ψ i : matter field, A i () coupling functions, «dilaton», Effective metric felt by energy i («observable» frame for i) g μν A i ( ) g μν Gravitation: spin (g μν )+ spin 0 () : NO SEP! Non-universal coupling (A gauge () A fermions (), etc.) : NO WEP NO SEP! * Gasperini 007, Damour & Polyakov 1994

13 The Hypothesis (In Einstein Frame) Energy content of the Universe is divided in 3 parts A gravitational sector described by pure spin (graviton) and spin 0 (dilaton) degrees of freedom and a matter sector containing : The ordinary matter (baryons, photons,...), ruled by the equivalence principle, defines the observable frame { } ( ) 4 μ S * μ ψ, * κ d x g R + S A g sector violating i the weak equivalence principle i [ ] S [ ψ, A ( ) g * ] 1 μν + A ( ) A ( ) (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- Invisible () sector has varying mass S μν [ ψ, g ] + S [ ψ, ( ) g ] 1 4 ω μν d x g ( Φ) R g Φ μφ ν Φ + S μν Φ a && m a dt a & g μν A ( ) g μν ( t ) A ( ) a ( t ), H ( t ) 1, da q ( t ) aa μν

14 Einstein Frame S κκ The Hypothesis: cosmological models μ { R } + S ψ, A ( ) 1 4 d x g * μ μν + [ g * ] S [ ψ, A ( ) g * ] The Action of the Hypothesis generalizes the models D-DE couplings Das, Corasaniti, Khoury 006: β Chameleon, Khoury, Weltman, Brax,Davis, van de Bruck 004: β A ( ) e, A ( ) e However the Hypothesis consider the scalar field is massless FLRW H A μν β ( ) A ( ) e, A ( ) 1 a& * & 8πG * a&& 8πG * + * * * * * + * a* 3 3 a* 3 6 * * ( ρ + ρ ), & ( ρ + 3p + ρ 3p ) a& * && + 3 & + 4πG* ( )( ρ* 3p* ) + 4πG* ( )( ρ* 3p* ) 0 a* Let us consider that the sector is a pressureless fluid and focus on the matter-dominated t dera of fthe universe D Conservation equations! & a& 3 a * * * ρ, + ρ, * ρ * A,,, C, ( ) 3 ( ) & ρ *, a * ρ BI 3 a

15 Dark Energy as a relaxation of the Weak Equivalence Principle on Cosmological Scales. The previous two fluids system can be rewritten as one field system We deduce ρ * '' + ' +ℵ 3 '² ( ) * * Α C ρ + ρ, Α A a * * T 3 d( Log( Α( )) d ( ) 0, ℵ( ) ( ) ( ) A ( ) + A ( ) + 1+ ( ) ( ) * ρ ( ) * ρ ( ), ' d d log a * ℵ, which corresponds to no violation of the WEP and/or if ρ * >> ρ * The present TST exibits a sophisticated convergence mechanism even in the case of very simple constitutive coupling functions TST in matter-dominated era are easily retrived if ( ) ( ) ( ) ℵ A ( ) ρ ( ) Ri A ( ) ρ ( ) A ( ) ( ) ( ), Ri + A ( ) ( ) 0 0

16 Dark Energy as a relaxation of the Weak Equivalence Principle on Cosmological Scales. GR-like attractors GR at CB Effective e potential ρ b ρ <<1 ρ b ρ >>1 (Gravitational coupling) Chameleon-like like Effect (Khoury & Weltman 004; ota & Shaw 006; Brax et al. 004; ota & Barrow 004). Relaxation of Weak Equivalence Principle on cosmological scales: ρ b ρ D <<1 Restricted WEP on visible matter («normally weighting» sector): ρ b ρ D >>1 One space-time but two couplings G and G («minimal» WEP violation) corresponding to different minima in the couplings functions

17 Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: Toward an unification to D and DE For any set of constitutive coulings functions, A (), A (), the resulting couling function A has at least one extremum and there exists a finite value of the effective gravitational coupling constant G which is different from GR. G c ( ) A ( ) ( ) k, ( ) k k A ( ) k ( A( ) ) C e + e, avec kak < 0 C ℵ dlog d The attracting value depends on the ratio of usual matter over abnormally weighting dust The attracting value depends on the ratio of usual matter over abnormally weighting dust and is intermediate between the value of for which A () extremum (when ρ* >>ρ *) and the value of for which A () is extremum (when ρ *<<ρ *).

18 Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: Astrophysical discussion The violation of the WEP strongly depends on the ratio of usual matter energy density over. As both usual matter and clusters, this violation is different with the scale considered. Furthermore, the 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 D at low scales. The domination of usual matter over D 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 D is sub-dominant, i.e. at low scales. We therefore conjecture that t GR is verified on the very small (sub-galactic) scales at which hthe 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 acceleration without t corrections due to the variation of the gravitational ti constant t 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 model.

19 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 D and DE Toward an unification to D and DE ( ) ( ) c G A G g A g μν μν *, * Observational Frame G ( ) ( ) T A T T A T μ ν ν μ μ ν ν μ *, * 4 4 A (quasi) Friedman description ( ) ( ) ( ) ( ) ( ) ' 3 ' ' ' 1 * ρ ρ π c G H H A a a H & ( ) ( ),, ' ' 3 8 ρ π Ω Ω Ω Ω c H G ' 3 3 ρ ρ ( ) 3 ' Accelating Universe in the Hypothesis FLRW-like but D not scaling in a -3 (varying mass), and Exotic DE tracking D and baryons Accelating Universe in the Hypothesis ( ) c d d G dt a d a ρ ρ π 3 ' ' 3 ' ( ) c G ρ ρ π 4 + Acceleration occurs in the observational frame, for instance, if <0 and ρ >>ρ

20 Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: Toward an unification to D and DE Type Ia supernovae Hubble diagram (Astier et al 006) μ z m 5log d 10 L z R i 0.11, R 0.31, Ω , Ω 0 0.6, t 0 (Gyr)15,9, χ /dof1.03 ( ) ( ) ΛCD Blue: data from SLNS Red: data from HST Gold sample Usual atter Baryon D G () DE

21 Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: Toward an unification to D and DE Type Ia supernovae Hubble diagram (HST + SNLS data) σ 1σ Usual atter Baryon D G () DE b 0.0 1σ Ω σ D Ω easurement of baryons and D distribution from SNe Ia alone! Independent predictions close to that of ΛCD with a very good agreement with BBN and CB

22 Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: A natural phantom universe An acelerating Universe in the hypothesis 1 d a a dt 8 H + 3 4πGc 4πG ρ T 3 3 π G c T DE ( ρ + ρ ) c ρ DE ( 1+ 3ω ) eff

23 Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: A unified description of D and DE Constraints from SNe Ia Hubble diagrams 3σ 3σ 1σ 1σ HST Gold DATA SNLS DATA Λ ruled out 1σ, σ (HST)! Ω in agreement with independant analysis!

24 Dark Energy as a relaxation of the Weak Equivalence Principle at cosmological scales: A natural phantom universe Constraints from SNe Ia Hubble diagrams σ σ 1σ 1σ Ω B Ω B HST Gold DATA SNLS DATA A natural phantom universe (super acceleration)! Ω B very good agreement with BBN and CB analysises

25 The Hypothesis Reducing Dark Energy to a new property of Dark atter: The Anomalous Gravity Open Question: Test of the equivalence principle on cosmological scales?

26 How discriminating between all Dark Energy odels? Implications on Structure Formation Dark atter as a time-dependent inertial mass ( ) ( ) A ( ) ( ) A ( ) m* A m Structure Formation. G N (t) Poisson Equation is modified Inertiel ass(t) Free Fall Equation is modified Observational Frame

27 A Keystone Between icrophysics and Gravitation? The most remarkable feature of our model is that, besides of its cosmological predictions, it allows us to deduce a new constraint relating microphysics and gravitation: To obtain the cosmological evolution described above, it is enough that the matter and coupling functions have to be inversely proportional: A ( ) A ( ) Where ρ R b ( t + ) is the ratio at which ordinaty matter and D ρ D densities freeze once the scalar field reaches the attractor Awe R From the cosmological data on supernovae, we find a R close to unity (at 68 % confidence level) l) R ( HST ), R ( SNLS)

28 A Keystone Between icrophysics and Gravitation? We deduce an intriguing relation between the constant mass of baryons m b and the changing D m D and gravitational strenght G c G ) G m m μ c ( x ) mb md ( xμ where the bar means the Earth laboratory value. N b D Although this relation does not fix the bare mass of D, it rules its scaling by imposing a conservation of the product of the gravitational charges of baryons and D. 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 the fundamental approaches that aim to unify gravity and microphysics with explicit space-time dependancies of masses and couplings.

29 Dark Energy and the * hypothesis Jean-ichel Alimi, i André Füzfa Thank you for your attention * means also Abnormally Weighting Energy

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31 4 ) Energy densities (GeV Baryons D Radiation DE Λ Scale Factor a