Konstantinos Dimopoulos

1. The quantum origin of cosmic structure: Theory and observations Konstantinos Dimopoulos Lancaster University

2. Hot Big Bang and Cosmic Inflation • Standard Model of Cosmology:Hot Big Bang + Cosmic Inflation • HBB: expansion, CMB, BBN, age • Cosmic inflation: horizon & flatness • Inflation: Brief superluminal expansion in the Early Universe Universe = large + uniform • Perfect uniformity no galaxies! • Deviation from uniformity needed: Primordial Density Perturbation •  evidence of the PDP in the CMB • Sachs-Wolfe effect: CMB redshifted when crossing growing overdensities Origin of PDP: Inflation again!

3. Horizon during inflation Event Horizon of inverted Black Hole Particle Production during Inflation Friedman Equation: vacuum density domination: End of inflation:  change of vacuum Vacuum states in inflationpopulated afterwards virtual particles real particles quantum fluctuations classical perturbations

4. Promote to operator: Equation of motion: • Solution: Particle Production during Inflation • Standard choice: free scalar field Perturb: Fourier Xform: before Horizon exit • Vacuum condition:

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

6. Classical evolution: freezing: Particle Production during Inflation → Scale invariance • Curvature Perturbation: same scale dependence Spectral Index: For light scalar field: WMAP observations:

7. The Curvature Perturbation • In GR curvature  density: depends on spacetime foliation • Gauge invariant curvature perturbation: • Power spectrum: WMAP • Bispectrum: • Non-linearity parameter: equilateral: local: WMAP

8. Inflation end: • Reheating:oscillations correspond to inflaton particles which decay to thermal bath of HBB Potential domination: The Inflationary Paradigm • The Universe undergoes inflation when dominated by the potential density of a scalar field (called the inflaton field) • For homogeneous scalar field: • Slow-Roll: flat direction required

9. Inflaton = light Slow Roll • Inflaton Perturbations Inflation ends at different times at different locations The Inflaton Hypothesis • The field responsible for the curvature perturbation also drives inflation Difference between uniform density and spatial flatness Spectral index: Non-Gaussianity: If non-G observed then single field inflation killed

10. The field responsible for the curvature perturbation is other than the inflaton (curvaton ) The Curvaton Hypothesis Lyth & Wands (2002) • The curvaton is a light field Curvaton = not ad hoc • Realistic candidates include RH-sneutrino, orthogonal axion, MSSM flat direction Spectral index: During inflation the curvaton’s contribution to the density is negligible The curvature perturbation depends on the evolution after inflation

11. During inflation the curvaton is frozen with • After inflation the curvaton unfreezes when • Afterwards decays to thermal bath of HBB The curvaton mechanism • After unfreezing the curvaton oscillates around its VEV • Oscillations = pressureless matter  curvaton (nearly) dominates the Universe at different times at different locations Non-Gaussianity: WMAP bound

12. l=5 in galactic coordinates l=5 in preferred frame Why not Vector Fields? • Tantalising evidence exists of a preferred direction in the CMB • Impossible to form with scalars • Also, despite their abundance in theories beyond SM, scalar fields are not observed as yet • What if Higgs not found in LHC? • Until recently Vector Fields not considered for particle production • Inflation homogenizes Vector Fields • Homogeneous Vector Field = in general anisotropic • Generation of large-scale anisotropy in conflict with CMB uniformity • Circumvented if Vector Field is subdominant during inflation • Light Vector Fields  conformally invariant  noparticle production •  model dependent mechanisms to break conformality

13. Solve with vacuum boundary conditions: & Lorentz boost factor: from frame with • Obtain power spectra: expansion = isotropic • Perturb: Polarization vectors: Particle Production of Vector Fields • Consider model with suitable breakdown of vector field conformality • Fourier Xform: • Promote to operator:

14. Case A: parity violating • Case B: parity conserving (most generic) isotropic particle production • Case C: • Statistical Anisotropy:anisotropic patterns in CMB Particle Production of Vector Fields Observations: weak bound Groeneboom and Eriksen (2009) • Cases A&B: vector field = subdominant statistical anisotropy only • Curvature perturbation due to Vector Field alone only in Case C

15. & • Transverse component: (Parity conserving) Scale invariance if: & Non-minimal coupling to Gravity KD & Karciauskas (2008) • Longitudinal component: Case B: The vector field can generate statistical anisotropy only • Model may suffer from instabilities (ghosts) Himmetoglu et al. (2009)

16. Motivates model even if vector field is not gauge boson Varying kinetic function and mass KD (2007) • Vector field remains light: • Maxwell kinetic term does not suffer from instabilities (ghost-free) at Horizon exit • Abelian massive vector field = renormalizable even if not a gauge field Scale invariance: Statistical anisotropy only (Case B) • Vector field becomes heavy: KD, Karciauskas, Wagstaff (2009) Particle production isotropic (Case C) No need for fundamental scalar field

17. & Inflation homogenises the vector field: harmonic oscillations Vector Curvaton Paradigm & [KD, PRD 74 (2006) 083502] Pressureless and Isotropic • Vector field domination occurs without introducing significant anisotropy • is imposed at (near) domination

18. : projection of on - plane Statistical Anisotropy and non-Gaussianity Karciauskas, KD and Lyth (2009) • Vector curvaton: • Non-Gaussianity = correlated with statistical anisotropy: Smoking gun • model: Predominantly anisotropic • model: identical to scalar curvaton

19. The Planck satellite will increase precision to: Conclusions • Cosmic structure originates from growth of quantum fluctuations during a period of cosmic inflation in the Early Universe • The particle production process generates an almost scale invariant spectrum of superhorizon perturbations of suitable fields • These pertubrations give rise to the primordial density/curvature perturbation via a multitude of mechanisms (inflaton, curvaton etc.) • Observables such as the spectral index or the non-linearity parameter will soon exclude whole classes of inflation models • Recently the possibility that vector fields contribute or even generate (vector curvaton) is being explored • Vector fields can produce distinct signatures such as statistical anisotropy in the CMB (bi)spectrum Planck precision: • Cosmological observations allow for detailed modelling and open a window to fundamental physics complementary to LHC