Primordial density perturbations from the vector fields Mindaugas
Primordial density perturbations from the vector fields Mindaugas Karčiauskas in collaboration with Konstantinos Dimopoulos Jacques M. Wagstaff
Plan ● Hot Big Bang and it’s problems; ● Primordial perturbations; ● Inflation and CMB parameters; ● New observable – statistical anisotropy; ● Vector curvaton model;
The Universe After 1 s ● The Universe is expanding; ● Universe started being hot; ● Big bang nucleosynthesis; ● Large scale structure formation;
The Universe After 1 s ● The Universe is expanding: ● Hubble’s discovery 1929; ● Current measurements: Freedman et al. (2001)
The Universe After 1 s ● The early universe was hot ● Discovery of the CMB; ● A. Penzias & R. Wilson (1965); ● Radiation which cooled down from ~3000 K to 2. 7 K; ● Steady State Cosmology is wrong;
The Universe After 1 s ● Big Bang Nucleosynthesis ● H, He, Li and Be formed during first 3 minutes; ● R. A. Alpher & G. Gamow (1948) ; ● Predictions span 9 orders of magnitude: ● Confirmed by CMB observations at ;
The Universe After 1 s ● Large Scale Structure formation ● Seed – perturbations of the order ; ● Subsequent growth due to gravitational instability;
Initial conditions for the Hot Big Bang ● Horizon – the universe is so uniform; ● Flatness – the universe is so old; ● Primordial perturbations – what is their origin;
Inflation ● Horizon – the universe is so uniform; ● Flatness – the universe is so old; ● Primordial perturbations – what is their origin; ==> Inflation: ll ll <==/
Superhorizon Density perturbations ● Perturbations are superhorizon TE cross correlation ● One can mimic acoustic peaks… Hu et al. (1997) ● … but not superhorizon correlations; ● => Inflation Barreiro (2009)
CMB – a Probe of Inflationary Physics ● What are the properties of primordial density perturbations and what can they tell about inflation? ● Random fields; ● The curvature perturbation: ● is conserved on super-horizon scales if .
Random Fields ● Curvature perturbations – random fields ; ● Isotropic two point correlation function: isotropic => ● Momentum space:
Correlation function ● Two point correlator in momentum space: ● The shape of the power spectrum: ● Inflation models => ● WMAP 5 yr measurements: ● Errorbars small enough to rule out some inflationary models
Higher Order Correlators ● Three point correlator: ● Non-Gaussianity parameter: ● Single field inflation => Gaussian perturbations: ● WMAP 5 yr measurements:
Statistical Anisotropy ● New observable; ● Anisotropic two point correlation function ● Anisotropic if for ● The anisotropic power spectrum: ● The anisotropic bispectrum:
Isotropic Random Fields with Statistical Anisotropy - preferred direction
Vector Field Model ● Until recently only scalar fields were considered for production of primordial curvature perturbations; ● We consider curvature perturbations from vector fields;
Vector Fields ● ● Vector fields not considered previously because: 1. Conformaly invariant => cannot undergo particle production; 2. Induces anisotropic expansion of the universe; 3. Brakes Lorentz invariance; Solved by using massive vector field: 1. Conformal invariance is broken; 2. Oscillates and acts as pressureless isotropic matter; 3. Decays before BBN;
Vector Curvaton Scenario ● The energy momentum tensor: I. Inflation II. Light Vector Field III. Heavy Vector Field IV. Vector Field Decay. Onset of Hot Big Bang
Particle Production ● Lagrangian ● De Sitter inflation with the Hubble parameter ; ● Three degrees of freedom: and ● If and => scale invariant perturbation spectra; ● At the end of inflation: and
Power Spectra
Anisotropic Perturbations ● Curvature perturbations statistically anisotropic; Groeneboom et al. (2009) => Vector contribution subdominant ● Non-Gaussianity: ● Correlated with statistical anisotropy ● Itself anisotropic ● Smoking gun for the vector field contribution to the curvature perturbations.
No Scalar Fields ● Curvature perturbations statistically isotropic; => No need for other sources of perturbations. ● Vector fields starts oscillating during inflation; ● Parameter space: ● Inflationary energy scale: ● Oscillations starts at least:
Summary ● Inflation – most successful paradigm for solving HBB problems and explaining the primordial density perturbations; ● New observable – statistical anisotropy; ● Massive vector curvaton model: ● Can produce the statistically anisotropic curvature perturbations: ● Non-Gaussianity is correlated with statistical anisotropy; ● Non-Gaussianity is itself anisotropic; ● Possible inflationary model building without scalar fields;
- Slides: 24