Modifications of gravity induced by abnormally weighting dark matter

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1 Modifications of gravity induced by abnormally weighting dark matter André Füzfa NAXYS & CP3 University of Namur-Louvain (Belgium) in collaboration with J.-M. Alimi (Obs. Paris), B. Famaey (Obs. Strasbourg), A. Hees (Obs. Brussels)

2 Why Dark Matter-Dark Energy interactions? Theoretical problems of the cosmological constant Λ Fine-tuning & coincidence, independent nature of DM & DE, origin of negative pressures, A cosmological mechanism for DE? Dynamical DE new degrees of freedom µ [T µ ν(m)+t µ ν(de)]=0 Separately conserved: QUINTESSENCE (only gravitational interaction) Conserved together: COUPLED DE Violation of the equivalence principles! µ T µ ν(m) 0 New interactions: toward a unified physics of the dark sector? Same physical nature for DM & DE ; new insights on coincidence and nature of DE Famous examples: Extended quintessence (Perrotta, et al., PRD , Riazuelo & Uzan, PRD ) Coupled DM-DE (Amendola, PRD ,Farrar & Peebles, ApJ ) Mass-Varying Neutrinos (MaVaNs), growing neutrinos (Fardon, Nelson, Weiner, JCAP ; Peccei, PRD ; Wetterich, Phys.Lett.B ; Amendola, Baldi, Wetterich PRD , etc.)

3 Gravitation without equivalence principles Equivalence principles : Universality of gravitation Einstein Equivalence Principle (EEP): Strong Equivalence Principle (SEP): + non-gravitational binding energies any type of binding energies SEP EEP SEP violation: EEP violation: Coupled DM-DE MaVaNs, chameleons, etc. Mm AWE Hypothesis Mm + mdm (xµ ) µ G(x ) No EEP no SEP m(xµ) G(xµ) ϕ(earth) = ϕ(moon) Gravitational binding energy: µ Egrav (x ) = G Non-universality of free fall Extended quintessence Brans-Dicke tensor-scalar theories V Mint (xµ ) dmsh (xµ ) r DM-induced SEP violation!

4 The anomalous weight of Dark Matter Interactions in the dark sector: Variation of DM mass violation of the Equivalence PrincipleS (EEP and SEP) No EEP : non-universality of free fall (DM vs ordinary matter) No EEP no SEP : variation of gravitational strength G DM-induced modifications of gravity!! Cosmic acceleration, galactic dynamics, local deviations from GR The AWE Hypothesis: a relaxed equivalence principle S grav = 1 gd4 x{ Φ R ω } BD(Φ) g µν µ Φ ν Φ 2 Φ [ ] S source =S m [ψ m, g µν ]+S awe ψawe,m 2 (Φ) g µν SEP violation (varying G) AWE also means «Abnormally Weighting Energy» EEP relaxation (mass-variation of dark sector) T. Damour, et al. PRL 64, 123 (1990) J.-M. Alimi, A. Füzfa, JCAP 0809 (2008) A. Füzfa, J.-M. Alimi, PRD (2007) A. Füzfa, J.-M. Alimi, PRL 97, (2006)

5 Induced modifications : 1) Cosmic acceleration Effective potential High ρ DM ρ m Matter-dominated era: m DM decreases such that ρ DM ρ baryons when a (GR-like) Attractors: EPs ok (GR-like) Standard FLRW expansion: ρ DM Low ρ m ϕ Cosmological evolution: A quest for the EP! Radiation-dominated era: ϕ attracted toward GR Cosmic acceleration requires large α 0 (large ϕ 0 )! AWE-driven cosmic expansion: Consistency with tests of GR? γ PPN -1~ α A α 0

6 Induced modifications : 2) Galactic dynamics Large α 0 (or ϕ 0 ) can be used as boundary condition for static problems in tensor-scalar gravity Such large value is incompatible with BBN constraints or convergence toward GR in USUAL tensor-scalar gravity (one coupling function) Long-ranged fifth force described by Poisson equation with densitydependent coupling ϕ= 4πρ m 2 ϕ Mach L Mach = m Mach (ρ) 1/2 Mach length: Typical length scale of ϕ Compatibility with GR: the scalar field has to be small around non-compact objects like galaxies, stars, planets, etc. Compacity sun =GM Sun /(R sun c²)~10-6 Compacity galaxy ~10-7 m Mach ~10 15 GeV~10-4 m Pl This huge sensitivity to the scalar field creates scalar charges α A that compensate for large α 0

7 Induced modifications : 2) Galactic dynamics Interesting phenomenological features for toy models: excess and wiggles Matter-dominated galaxy α(r=8kpc)=10-4 AWE DM-dominated galaxy Excess in circular velocity is related to scalar field gradient and thus outskirts density => flattening possible for which profile? Wiggles: oscillations of scalar field can be seen in rotation curves Galactic dynamics predicts solar system deviations from GR

8 Induced modifications : 3) local deviations from GR Thin shell effect β PPN -1~10-7 Accounting for cosmology and (hopefully) for galaxy rotation curves yield deviations from GR that are at hand of present tests!

9 Conclusions AWE Hypothesis: dark matter induced modifications of gravity Non-universal scalar-tensor theory Modified cosmological convergence mechanism & «Chameleon» effect Cosmic acceleration, galactic dynamics, local departures from GR Advantage: easy to model (1 additional Poisson equation + redefinitions of observables) Modifications of gravity on galactic scales yield testable deviations from GR Perspectives To flatten rotation curves : reintroduce a sub-dominant DM component Explore modifications on cluster scales Galactic scalar charges: modified external dynamics non-universality of free fall for DM modified gravitational lensing, etc. spontaneous scalarisation of DM around galactic center Thank you for your attention!

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