1. Konstantinos Dimopoulos Lancaster University

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

3. Hot Big Bang and Cosmic Inflation Cosmological Principle: The Universe is Homogeneous and Isotropic Cosmological Principle: The Universe is Homogeneous and Isotropic Horizon Problem: Uniformity over causally disconnected regions Horizon Problem: Uniformity over causally disconnected regions Cosmic Inflation: Brief period of superluminal expansion of space 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 The CMB appears correlated The CMB appears correlated on superhorizon scales on superhorizon scales (in thermal equilibrium at (in thermal equilibrium at preferred reference frame) preferred reference frame)  Incompatible with Finite Age

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

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

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

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

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

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

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

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

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

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

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

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

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

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

18. Particle Production of Vector Fields Conformal Invariance: vector field does not couple to metric (virtual particles not pulled outside Horizon during inflation) Breakdown of conformality of massless vector field is necessary Breakdown of conformality of massless vector field is necessary Mass termnot enoughno scale invariance Find eq. of motion for vector field perturbations: Find eq. of motion for vector field perturbations: Promote to operator: Polarization vectors: Canonical quantization: Fourier transform: (e.g.,, or ) Typically, introduce Xterm : Typically, introduce Xterm :

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

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

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

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

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