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Konstantinos Dimopoulos

Vector Fields and the. Curvature Perturbation in the Universe. Konstantinos Dimopoulos. Lancaster University. Expanding Universe:. Finite Age:. CMB Anisotropy:. Hot Big Bang and Cosmic Inflation. Hot Early Universe: CMB. On large scales: Universe = Uniform.

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Konstantinos Dimopoulos

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  1. Vector Fields and the Curvature Perturbation in the Universe Konstantinos Dimopoulos Lancaster University

  2. Expanding Universe: • Finite Age: • CMB Anisotropy: Hot Big Bang and Cosmic Inflation • Hot Early Universe: CMB • On large scales: Universe = Uniform • Structure: smooth over 100 Mpc: Universe m Fractal

  3. Hot Big Bang and Cosmic Inflation • Cosmological Principle:The Universe is Homogeneous and Isotropic • Incompatible with Finite Age • Horizon Problem:Uniformity over causally disconnected regions • The CMB appears correlated on superhorizon scales (in thermal equilibrium at preferred reference frame) • Cosmic Inflation:Brief period of superluminal expansion of space • Inflation produces correlations over superhorizon distances by expanding an initially causally connected region to size larger than the observable Universe

  4. Horizon during inflation Event Horizon of inverted Black Hole After Horizon exit: quantum fluctuations classical perturbations • Sachs-Wolfe: CMB redshifted when crossing overdensities Hot Big Bang and Cosmic Inflation • Inflation imposes the Cosmological Principle • C. Principle = no galaxies! • Where do they come from? • Inflation + Quantum Vacuum • Quantum fluctuations (virtual particles) of light fields exit the Horizon

  5. Equation of motion for homogeneous scalar : Klein - Gordon Friedman equation: exponential expansion (quasi) de Sitter inflation Potential density domination: Slow – Roll inflation: The Inflationary Paradigm • The Universe undergoes inflation when dominated by the potential density of a scalar field (called the inflaton field) A flat direction is required

  6. Solving the Flatness Problem • Flatness Problem: The Universe appears to be spatially flat despite the fact that flatness is unstable • Inflation enlarges the radius of curvature to scales much larger than the Horizon

  7. Inflation terminates when: • Reheating: After the end of inflation the inflaton field oscillates around its VEV. These coherent oscillations correspond to massive particles which decay into the thermal bath of the HBB The end of Inflation Reheating must occur before BBN

  8. Perturb: Fourier transform: Promote to operator: Canonical quantization: Equation of motion: well before Horizon exit • Solution: Particle Production during Inflation • Semi-classical method for scalar fieds • Vacuum boundary condition:

  9. Superhorizon limit: • Power spectrum: Light field: Scale invariance: Particle Production during Inflation Hawking temperature

  10. Classical evolution: same scale dependence Spectral Index: freezing: WMAP satellite observations: Particle Production during Inflation → Scale invariance • Curvature Perturbation:

  11. Inflaton = light Slow Roll • Inflaton Perturbations Inflation is terminated at different times at different points in space Slow Roll: The Inflaton Hypothesis • The field responsible for the curvature perturbation is the same field which drives the dynamics of inflation Tight constraint → Fine tuning

  12. The field responsible for the curvature perturbation is a field other than the inflaton (curvaton field ) Curvature Perturbation: where The curvature perturbation depends on the evolution after inflation The Curvaton Hypothesis • The curvaton is a light field • Realistic candidates include RH-sneutrino, orthogonal axion, MSSM flat direction Curvaton = not ad hoc During inflation the curvaton’s conribution to the density is negligible

  13. During inflation the curvaton is frozen with • After inflation the curvaton unfreezes when • Afterwards decays into the thermal bath of the HBB Inflation fine-tuning becomes alleviated Merits: The inflaton field may not be light and bound only on the inflation scale: The curvaton mechanism • After unfreezing the curvaton oscillates around its VEV • Coherent curvaton oscillations correspond to pressureless matter which dominates the Universe imposing its own curvature perturbation

  14. e.g. inflation due to geometry: gravity ( - inflation) Scalar vs Vector Fields • Scalar fields employed to address many open issues: inflationary paradigm, dark energy (quintessence) baryogenesis (Affleck-Dine) • Scalar fields are ubiquitous in theories beyond the standard model such as Supersymmetry (scalar parteners) or string theory (moduli) • However,no scalar field has ever been observed • Designing models using unobserved scalar fields undermines their predictability and falsifiability, despite the recent precision data • The latest theoretical developments (string landscape) offer too much freedom for model-building • Can we do Cosmology without scalar fields? • Some topics are OK: Baryogenesis , Dark Matter , Dark Energy (ΛCDM) • Inflationary expansion without scalar fields is also possible: • However, to date,no mechanism for the generation of the curvature/density perturbation without a scalar field exists

  15. l=5 in galactic coordinates l=5 in preferred frame Why not Vector Fields? • Inflation homogenizes Vector Fields • To affect / generate the curvature perturbation a Vector Field needs to (nearly) dominate the Universe • Homogeneous Vector Field = in general anisotropic • Basic Problem:the generatation of a large-scale anisotropy is in conflict with CMB observations • However, An oscillating massive vector field can avoid excessive large-scale anisotropy • Also, some weak large-scale anisotropy might be present in the CMB (“Axis of Evil”):

  16. Massive vector field: Abelian vector field: Equations of motion: Flat FRW metric: Inflation homogenises the vector field: & Klein-Gordon Massive Abelian Vector Field • To retain isotropy the vector field must not drive inflation Vector Inflation [Golovnev et al. (2008)] uses 100s of vector fields

  17. & • Eq. of motion: harmonic oscillations Vector Curvaton • Vector field can be curvaton if safe domination of Universeis possible Pressureless and Isotropic • Vector field domination can occur without introducing significant anisotropy. The curvature perturbation is imposed at domination

  18. Mass term not enough no scale invariance (e.g. , , or ) • Typically, introduce Xterm : • Find eq. of motion for vector field perturbations: Fourier transform: Promote to operator: Polarization vectors: Canonical quantization: Particle Production of Vector Fields • Breakdown of conformality of massless vector field is necessary Conformal Invariance: vector field does not couple to metric (virtual particles not pulled outside Horizon during inflation)

  19. Solve with vacuum boundary conditions: & Lorentz boost factor: from frame with • Obtain power spectra: expansion = isotropic • Case A: parity violating • Case B: parity conserving (most generic) isotropic particle production • Case C: • Statistical Anisotropy: anisotropic patterns in CMB Observations: weak bound • Vector Curvaton = solely resonsible for only in Case C Particle Production of Vector Fields • Cases A&B: vector curvaton = subdominant: statistical anisotropy only

  20. & Perturb & Fourier Xform Eq. of motion: • Transverse component: (Parity conserving) Scale invariance if: & Non-minimally coupled Vector Curvaton

  21. Case B: The vector curvaton contribution to must be subdominant Non-minimally coupled Vector Curvaton • Longitudinal component: • The vector curvaton can be the cause of statistical anisotropy saturates observational bound

  22. Non-Gaussianity in scalar curvaton scenario: • Observations: The Planck sattelite will increse precision to: & measure of parity violation : projection of unit vector onto the - plane • Ruduction to scalar curvaton case if: & • Non-minimally coupled case: Statistical Anisotropy and non-Gaussianity • Non Gaussianity in vector curvaton scenario: • Non-Gaussianity = correlated with statistical anisotropy: Smoking gun

  23. The vector field can act as a curvaton if, after inflation, its mass becomes: ( zero VEV: vacuum = Lorentz invariant ) Conclusions • A vector field can contribute to the curvature perturbation • In this case, the vector field undergoes rapid harmonic oscillations during which it acts as a pressureless isotropic fluid • Hence, when the oscillating vector field dominates, it introduces negligible anisotropy (“Axis of Evil”?) • If particle production is isotropic then the vector curvaton can alone generate the curvature perturbation in the Universe • If particle production is anisotropic then the vector curvaton can give rise to statistical anisotropy, potentially observable by Planck • Correlation of statistical anisotropy and non-Gaussianity in the CMB is the smoking gun for the vector curvaton scenario • The challenge is to obtain candidates in theories beyond the standard model, which can play the role of the vector curvaton Physical Review D 74 (2006) 083502 : hep-ph/0607229 arXiv:0806.4680 [hep-ph] Physical Review D 76 (2007) 063506 : 0705.3334 [hep-ph] arXiv:0809.1055 [astro-ph] Journal of High Energy Physics 07 (2008) 119 : 0803.3041 [hep-th]

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