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

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!

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 Horizon during inflation Event Horizon of inverted Black Hole quantum fluctuations classical perturbations

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

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

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

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

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: Potential domination: Slow-Roll: flat direction required Inflation end: Reheating: oscillations correspond to inflaton particles which decay to thermal bath of HBB

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

The Curvaton Hypothesis The field responsible for the curvature perturbation is other than the inflaton (curvaton ) 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

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

Why not Vector Fields? Tantalising evidence exists of a preferred direction in the CMB l=5 in preferred frame l=5 in galactic coordinates 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  no particle production  model dependent mechanisms to break conformality

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

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

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

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

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

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

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 The Planck satellite will increase precision to: 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