Dark Energy vs. Dark Matter: Towards a unifying scalar field? Alexandre ARBEY Centre de Recherche Astrophysique de Lyon Institut de Physique Nucléaire de Lyon, March 2nd, 2007.
Introduction The Dark Stuff Problems Dark Matter Dark Energy Scalar Fields as Dark Energy Quintessence Scalar Fields as Dark Matter Massive complex scalar fields. Massive and self-interacting complex scalar fields. Dark Matter vs. Dark Energy: A Dark Fluid as a possible reconciliation?
Ia. The Dark Matter Problem Galactic Scale The most striking problems arrive from the Galaxy Rotation Curves.
Large Spiral Galaxies Galaxy Rotation Curves = Rotation velocity of stars Corbelli & Salucci Dwarf Spiral Galaxies >> Carignan et al. Well-known baryonic contribution
Ia. The Dark Matter Problem Galactic Scale The most striking problems arrive from the Galaxy Rotation Curves. 90 % of the effective matter is invisible! Clusters Scale At this scale, the existence of a great amount of non-visible matter can be deduced from cluster gas and weak lensing observations.
Dark Matter in Clusters X-Ray observations presence of hot gas (P, ρ, T) ROSAT >> Spherical cluster in hydrostatic equilibrium Weak lensing Approximately the same results!
Ia. The Dark Matter Problem Galactic Scale The most striking problems arrive from the Galaxy Rotation Curves. 90 % of the effective matter is invisible! Clusters Scale At this scale, the existence of a great amount of non-visible matter can be deduced from cluster gas and weak lensing observations. Cosmological Studies Same conclusions! Different studies enable to know the proportions of baryonic and non-baryonic matters in the global energy of the cosmic fluids.
Cosmological Standard Model Friedmann-Lemaître Universe Homogeneous and Isotropic Universe Robertson-Walker Metric: Cosmic fluids: matter, cosmological constant, radiation (ρ, P) Einstein Equations z : redshift Today: critical density Cosmological parameter (for each fluid): Curvature: : closed Universe : open Universe
Supernovae of type Ia Cosmic Microwave Background (CMB) Maps of the anisotropies Angular Power Spectrum WMAP Team WMAP Team
Cosmological Parameters The Universe is approximately flat! SCP WMAP
Ia. The Dark Matter Problem Galactic Scale The most striking problems arrive from the Galaxy Rotation Curves. 90 % of the effective matter is invisible! Clusters Scale At this scale, the existence of a great amount of non-visible matter can be deduced from cluster gas and weak lensing observations. Cosmological Studies Same conclusions! Different studies enable to know the proportions of baryonic and non-baryonic matters in the global energy of the cosmic fluids. 30 % of the total energy in the Universe is Matter. 10 % of this Matter is baryonic!
Ia. The Dark Matter Problem What is the Nature of the Dark Matter?
Dark Matter Models Baryonic Dark Matter Dark Matter in galaxies and clusters would be in fact baryonic matter, taking the form of cold gas or non-luminous massive objects.
Baryonic Dark Matter Galaxies and clusters could be full of gases The interstellar medium is full of HI. Dark matter densities in galaxies seem to follow the HI densities. H 2 is difficult to detect, and underestimated. Stellar radiation could heat the gas or evaporate it. There could be massive and compact objects. Black Holes (center of galaxies ) or dark stars (dwarves ) Objects of mass inferior to 30 solar masses are not sufficient. But Problem with the cosmological observations! Need for a non-baryonic and more exotic matter!
Dark Matter Models Baryonic Dark Matter Dark Matter in galaxies and clusters is in fact baryonic matter, taking the form of cold gas or non-luminous massive objects. WIMPs Dark Matter consists in weakly interacting massive particles from new particle physics models (like Supersymmetry).
WIMPs Weakly Interacting Massive Particles Good cosmological behavior and good galaxy formation Rotation curves at large radius for large galaxies Clusters OK Not detected yet. Questions about clumpiness (clumps formation, cuspy galaxy core ) Supersymmetric Standard Model Standard Model extension Predicts high-mass particles Cold Dark Matter Not verified yet
Dark Matter Models Baryonic Dark Matter Dark Matter in galaxies and clusters is in fact baryonic matter, taking the form of cold gas or non-luminous massive objects. WIMPs Dark Matter consists in weakly interacting massive particles from new particle physics models (like Supersymmetry). Other : axions,... Dark Matter may be composed of even more exotic particles. Modified Gravitation Laws Dark Matter does not exist. The gravitation laws have to be changed.
Ib.. The Dark Energy Problem 70 % of the total energy in the Universe has a negative pressure! Geometry Cosmology Energy 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?
Quintessence (1) Quintessence= real homogeneous scalar field Friedmann equations + Klein-Gordon equation Usual potentials:
Quintessence (2) Theoretical Constraints: no fine tuning in the potential no fine tuning in the initial conditions today, Observational Constraints: Cosmic Microwave Background Large Scale Structures Gravitational lensing Supernovae of Type Ia
Quintessence (3) radiation Inverse Power Law Inverse Power Law matter SUGRA SUGRA No definitive answer yet!
II. Scalar Fields as Dark Matter Arbey, Lesgourgues & Salati, Phys. Rev. D 64, 123528 - Phys. Rev. D 65, 083514 - Phys. Rev. D 68, 023511 Motivations
Motivations: The Cosmological Problems Dark Energy Archetypical model : quintessence real scalar field Repulsing effect on the dynamics of the Universe Dark Matter Binding effect on the dynamics of the Universe Need for smooth weakly interacting Dark Matter densities Hint: Boson stars example Scalar Fields coherent states like Bose condensates. Are scalar fields able to solve both problems? Hope for a common explanation!
II. Scalar Fields as Dark Matter Arbey, Lesgourgues & Salati, Phys. Rev. D 64, 123528 - Phys. Rev. D 65, 083514 - Phys. Rev. D 68, 023511 Motivations Massive Complex Scalar Fields Galaxy Rotation Curves Cosmological Behavior
A. Massive Complex Scalar Field Quadratic potential Galaxy Rotation Curves (1) Spherical symmetry: Static isotropic metric: Klein-Gordon equation: Einstein equations:
Galaxy Rotation Curves (2) Resolution discrete number of solutions, i.e. fundamental and excited states To ensure stability, one will consider only the fundamental and less-energetic state, n=0. Newtonian limit Rotation curves:
Galaxy Rotation Curves (3) 3 parameters: m the mass of the scalar field, σ at the center (related to ω), and the baryonic density of stars at the centre. Universal Rotation Curves (Persic, Salucci & Stel) χ 2 comparison The favored mass m is around 10-23 ev! Confirmed by the study of the rotation curve of DDO 154
Cosmological Behavior Friedmann-Lemaître Universe with homogeneous radiation and scalar field densities. Internal rotation: Friedmann equation: with Klein-Gordon equation: ρ a 6 ρ a 3 The field has a good matter-behavior since the recombination!
II. Scalar Fields as Dark Matter Arbey, Lesgourgues & Salati, Phys. Rev. D 64, 123528 - Phys. Rev. D 65, 083514 - Phys. Rev. D 68, 023511 Motivations Massive Complex Scalar Fields Galaxy Rotation Curves Cosmological Behavior Massive and Self-Interacting Complex Scalar Fields Galaxy Rotation Curves Cosmological Behavior
B. Self-Interactive Scalar Field Quartic potential Galaxy Rotation Curves (1) Axisymmetric system: Klein-Gordon + Einstein + Newtonian approximation Heaviside Function Non-linear Modified Poisson Equation Galaxy dependent (equivalent to ω) Flattened exponentially decreasing baryonic densities (gas + stars)
Dwarf Spiral DDO 154 Galaxy Rotation Curves (2) Relatively well-known baryonic densities χ 2 200 χ 2 55 Navarro, Frenk and White profile Isothermal profile χ 2 500 χ 2 16 Rescaled gas density Our model m 4 /λ = 75 ev 4
Galaxy Rotation Curves (3) Stars + rescaled HI Gas densities Small galaxies χ 2 7 Best fits for: m4 λ 50 ev Maximum halo extension around 7.5 kpc! (Maximum extension λ/m 4!) 4 N7339 M-3-1042 N755 116-G12 563-G14 545-G5
Cosmological Behavior Friedmann-Lemaître Universe with homogeneous radiation and scalar field densities. Internal rotation: Friedmann equation: Scalar field density: Klein-Gordon equation: ρ a 4 ρ a 3 Behave like one extra neutrino family! The field has a good matter-behavior since the recombination!
Dark Matter Scalar Field: Summary Good results for the rotation curves of small galaxies. Good cosmological behavior. Consequences in the Solar System quartic potential in large galaxies need for a small value of m 4 /λ quartic potential in cosmology best for a large value of m 4 /λ Gravitational Lensing Structure Formation Coupling to Baryonic Matter Unification of the cosmological scalar fields?
III. Dark Fluid? A. Arbey, astro-ph/0506732 One unique fluid to replace Dark Matter and Dark Energy Constraints Today: Matter behaviour at local scales. Repulsing behaviour at cosmological scales. Early Universe: Matter behaviour at all scales. Advantages One unique Dark Fluid instead of two. Can lead to a High Energy Physics Theory. ω dark fluid > 1
Towards a unification? (1) with Attractive inside structures Repulsive in empty space Repulsive on cosmological scales seems possible to unify both visions within an inhomogeneous scenario!
Towards a unification? (2) A. Arbey, astro-ph/0506732 Equation of state: Low redshift: Supernovae of Type Ia Structure formation Big-Bang Bang Nucleosynthesis
Complex scalar field Unifying Scalar Field (1) Superposition of potentials A. Arbey, Phys. Rev. D 74, 043516 Local scales Cosmological scales
Unifying Scalar Field (2) Promising potential: A. Arbey, Phys. Rev. D 74, 043516 Local scales (galaxies) Local scales (clusters) Cosmological scales
Unifying Scalar Field (3) A. Arbey, Phys. Rev. D 74, 043516 Correct cosmological behavior
Unifying Scalar Field (3) A. Arbey, Phys. Rev. D 74, 043516 Correct cosmological behavior
Unifying Scalar Field (3) A. Arbey, Phys. Rev. D 74, 043516 Correct behavior at galactic scales
Complex scalar field Quantum Corrections (1) A. Arbey & F. Mahmoudi, submitted to Phys. Rev. D Effective potential method Effective action Effective potential
Quantum Corrections (1) Cosmological scalar fields: A. Arbey & F. Mahmoudi, submitted to Phys. Rev. D One-loop effective potential Λ = momentum cutoff ( = M Planck ) negligible
Quantum Corrections (2) A. Arbey & F. Mahmoudi, submitted to Phys. Rev. D Application to the dark fluid potential Effective dark fluid potential Shape modified by the quantum corrections! Way out: the quantumproof dark fluid potential! Or perhaps the initial potential was already effective
Quantum Corrections (3) Coupling to fermions? A. Arbey & F. Mahmoudi, submitted to Phys. Rev. D Effective potential Quantum-resistibility condition (GUT scale) Severely restricted
Conclusion Unifying Dark Fluids can be compatible with observations Many constraints on the models: - constraints on the matter behaviour - constraints on the dark energy behaviour - inhomogeneous modelization: local vs. global - quantum behaviour Examples of possible Dark Fluids: - Scalar fields with specific potentials - Chaplygin Gas,? More tests are needed