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Konstantinos Dimopoulos

Cosmological Perturbations. from a Vector Field. Konstantinos Dimopoulos. Lancaster University. e.g. inflation due to geometry: gravity ( - inflation). Scalar vs Vector Fields.

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Konstantinos Dimopoulos

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  1. Cosmological Perturbations from a Vector Field Konstantinos Dimopoulos Lancaster University

  2. 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 partners) 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

  3. 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”):

  4. 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

  5. & • 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

  6. 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)

  7. 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 responsible for only in Case C Particle Production of Vector Fields • Cases A&B: vector curvaton = subdominant: statistical anisotropy only

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

  9. 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

  10. Non-Gaussianity in scalar curvaton scenario: • Observations: The Planck satellite will increase precision to: & & : projection of unit vector onto the - plane • Reduction 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

  11. 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] arXiv:0812.0264 [astro-ph]

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