The Unifying Dark Fluid Model

Transcription

1 The Model Centre de Recherche Astrophysique de Lyon Invisible Universe Paris July 2nd, 2009

2 s Dark Matter Problem Dark Matter Dark Energy Dark Fluids? Different scales involved Galactic scale Galaxy Rotation Curves Galaxy Collisions Cluster Scale X-Ray Observations Weak Lensing Bullet Cluster Cosmological Scale Supernovæ of type Ia Cosmic Microwave Background...

3 s Dark Matter Candidates Dark Matter Dark Energy Dark Fluids? Baryonic Dark Matter WIMPs Other particles/fields: axions, Kaluza-Klein particles,... Exotic and non-baryonic particles Modified Gravitation Laws MOND, TeVeS, Scalar-tensor theories, Extra-dimensions, Brane worlds,...

4 s Dark Energy Problem Dark Matter Dark Energy Dark Fluids? 72% of the Universe energy has a negative pressure! Cosmological Constant A new physics constant... Vacuum Energy Applying Quantum Field Theory to Dark Energy? Not very Successful yet... Quintessence Dark energy as a real scalar field?...

5 Quintessence Dark Problems s Dark Matter Dark Energy Dark Fluids? Quintessence = real homogeneous scalar field Lagrangian density: L = g µν µ ϕ ν ϕ V (ϕ) { ρϕ = 1 Density and pressure: 2 ϕ2 + V (ϕ) P ϕ = 1 2 ϕ2 V (ϕ) ( ) 2 ȧ Friedmann equations: a = 8πG 3 ρ k a 2 ä a = 3πG 3 ( ρ + 3 P) Klein-Gordon equation: ϕ + 3H ϕ + V ϕ = 0 Usual potentials: V (ϕ) = αϕ β V (ϕ) = α exp( βϕ) V (ϕ) = α [cosh(βϕ) 1] n

6 Dark Fluids? Dark Problems s Dark Matter Dark Energy Dark Fluids? What if Dark Matter and Dark Energy are in interaction?

7 Dark Fluids? Dark Problems s Dark Matter Dark Energy Dark Fluids? What if they are different aspects of a same dark component?

8 Dark Fluids? Dark Problems s Dark Matter Dark Energy Dark Fluids? To answer these questions, we need to model the interactions

9 Dark Fluids? Dark Problems s Dark Matter Dark Energy Dark Fluids? Dark fluid: One unique fluid to replace dark energy and dark matter

10 Dark Fluids? Dark Problems s Dark Matter Dark Energy Dark Fluids? Must satisfy the observational constraints Today: Matter behaviour at local scales Repulsing behaviour at cosmological scales In the Early Universe: Matter behaviour at all scales.

11 Dark Fluids? Dark Problems s Dark Matter Dark Energy Dark Fluids? Advantages One unique Dark Fluid instead of two... Model dark energy / dark matter interactions Can be made up of scalar field!

12 s Massive Complex Scalar Field Massive and Complex Scalar Field L = g µν µ φ ν φ V (φ) V (φ) = m 2 φ 2 A. Arbey, J. Lesgourgues & P. Salati, Phys. Rev. D 64, Phys. Rev. D 65, Phys. Rev. D 68,

13 s Galaxy Rotation Curves (1) Massive Complex Scalar Field Internal rotation: φ( x, t) = σ(r) 2 e iωt Static and isotropic metric: dτ 2 = e 2u dt 2 e 2v { dr 2 + r 2 dθ 2 + r 2 sin 2 θdϕ 2 } Klein-Gordon equation: e 2v { σ + ( u + v + 2 )} r + ω 2 e 2u σ m 2 σ = 0 Einstein equations: { 2v + v 2 + 4v r = 8πGe 2v e 2u ω2 σ e 2v σ u + v + [ u r (u + v ) = ] } 8πG {e 2v e 2u ω2 σ 2 2 e 2v σ 2 m2 σ ρ baryon 2 + m2 σ 2 2 }

14 s Galaxy Rotation Curves (2) Massive Complex Scalar Field Resolution discrete number of solutions, i.e. fundamental and excited states To ensure stability, we consider only the fundamental and less-energetic state, n=0 Newtonian limit: ω 2 m 2 P (ω 2 m 2 )σ 2 0 Rotation curves obtained with: v 2 (r) = r r Φ grav(r) = rc 2 u (r)

15 s Galaxy Rotation Curves (3) Massive Complex Scalar Field Universal Rotation Curves (Persic, Salucci & Stel) The favoured mass is around ev! Confirmed by the study of the rotation curve of DDO 154

16 s Cosmological Behaviour Massive Complex Scalar Field Friedmann-Lemaître Universe with radiation and scalar field Internal rotation: φ(t) = σ(t) 2 e iθ(t) Friedmann equation: { 3H 2 = 8πG(ρ γ + ρ φ ) ( with ρ φ = 1 dσ ) 2 ( 2 dt + dθ ) 2 } dt σ 2 + m 2 σ 2 { d 2 σ + Klein-Gordon equation: 3 da dσ dt 2 a dt dt + m 2 σ ( ) dθ 2 dt σ = 0 d 2 θ σ + 3 da dθ dt 2 a dt dt σ + 2 dθ dσ dt dt = 0 The field has an adequate matter behaviour since recombination!

17 Collisions Dark Problems s Massive Complex Scalar Field C. Palenzuela, I. Olabarrieta, L. Lehner, S. Liebling, Phys. Rev. D75 (2007) e-05 6e-05 4e-05 2e x t = y e-05 6e-05 4e-05 2e x t = y x t = y Very complex systems, difficult to simulate! x t = y

18 s Towards Unification ρ cosmo (t 0 ) g.cm 3 ρ Milky Way ( r, t 0 ) g.cm 3 Towards Unification Unifying Scalar Field } ρ galaxy ρ cosmo Need for an inhomogeneous scenario! ω φ P φ ρ φ ω φ (a) ω 0 φ + (1 a)ωa φ Observational constraints: Dark Fluid parameters Ω 0 φ ωφ 0 ωφ a = ± = 0.80 ± 0.12 = 0.9 ± 0.5 A. Arbey, astro-ph/ A. Arbey, Open Astron. J. 1, 27

19 s Unifying Scalar Field (1) Towards Unification Unifying Scalar Field Complex Scalar Field L = g µν µ φ ν φ V (φ) Tentative potentials: V (φ) = m 2 φ 2 + α φ β V (φ) = m 2 φ 2 + α exp( β φ ) V (φ) = m 2 φ 2 + α [cosh(β φ ) 1] n m 2 φ 2 : responsible for the local scale behaviour The other term determines the cosmological behaviour A. Arbey, Phys. Rev. D 74,

20 s Unifying Scalar Field (2) Towards Unification Unifying Scalar Field Promissing potential: V (φ) = m 2 φ 2 + Ae B φ 2 m fixed by galaxy scales: m ev B fixed by cluster scales: B ev 2 dark energy A fixed by cosmological scales: A ρ0 A. Arbey, Phys. Rev. D 74,

21 s Cosmological Behaviour Towards Unification Unifying Scalar Field Correct cosmological behaviour

22 s Cosmological Behaviour Towards Unification Unifying Scalar Field Correct cosmological behaviour

23 Local Behaviour Dark Problems s Towards Unification Unifying Scalar Field Correct behaviour at galactic scales

24 s Quantum Corrections Towards Unification Unifying Scalar Field Coupling to fermions? L fermion = Ψ (x)[iγ µ µ γ 5 m f (Φ)]Ψ(x) Effective potential (effective field theory approach): V 1 loop (Φ cl ) = V (Φ cl ) Λ2 f 8π 2 [m f (Φ cl )] 2 with Λ f : momentum cutoff

25 s Quantum Corrections Towards Unification Unifying Scalar Field Coupling to fermions? L fermion = Ψ (x)[iγ µ µ γ 5 m f (Φ)]Ψ(x) Effective potential (effective field theory approach): V 1 loop (Φ cl ) = V (Φ cl ) Λ2 f 8π 2 [m f (Φ cl )] 2 with Λ f : momentum cutoff Quantum-resistivity condition: m f (Φ cl ) = m 0 f + δm f (Φ cl ) For Λ f 10 3 M Planck and m 0 f 100 GeV: δm f (Φ cl ) GeV OR: δm f (Φ cl ) Φ cl 2 or δm f (Φ cl ) exp( B Φ cl 2 ) Severely restricted!

26 s Many Constraints on these models Constraints on the matter behaviour Constraints on the dark energy behaviour Inhomogeneous modeling: local vs. large scales Quantum behaviour/coupling to fermions? Perspectives Scalar field dark fluid: Structure formation scenario Scalar field dark fluid: finding an adequate potential Relations with quantum field theory, quantum gravity, brane theories? Triple unification: dark energy + dark matter + inflaton?