1. Primordial density perturbations from the vector fields Mindaugas Karčiauskas in collaboration with Konstantinos Dimopoulos Jacques M. Wagstaff Mindaugas Karčiauskas in collaboration with Konstantinos Dimopoulos Jacques M. Wagstaff

2. Plan ● Hot Big Bang and it’s problems; ● Primordial perturbations; ● Inflation and CMB parameters; ● New observable – statistical anisotropy; ● Vector curvaton model; ● Hot Big Bang and it’s problems; ● Primordial perturbations; ● Inflation and CMB parameters; ● New observable – statistical anisotropy; ● Vector curvaton model;

3. The Universe After 1s ● The Universe is expanding; ● Universe started being hot; ● Big bang nucleosynthesis; ● Large scale structure formation; ● The Universe is expanding; ● Universe started being hot; ● Big bang nucleosynthesis; ● Large scale structure formation;

4. The Universe After 1s ● The Universe is expanding: ● Hubble’s discovery 1929; ● Current measurements: Freedman et al. (2001) ● The Universe is expanding: ● Hubble’s discovery 1929; ● Current measurements: Freedman et al. (2001)

5. The Universe After 1s ● The early universe was hot ● Discovery of the CMB; ● A. Penzias & R. Wilson (1965); ● Radiation which cooled down from ~3000K to 2.7K; ● Steady State Cosmology is wrong; ● The early universe was hot ● Discovery of the CMB; ● A. Penzias & R. Wilson (1965); ● Radiation which cooled down from ~3000K to 2.7K; ● Steady State Cosmology is wrong;

6. The Universe After 1s ● 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 ; ● 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 ;

7. The Universe After 1s ● Large Scale Structure formation ● Seed – perturbations of the order ; ● Subsequent growth due to gravitational instability; ● Large Scale Structure formation ● Seed – perturbations of the order ; ● Subsequent growth due to gravitational instability;

8. 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; ● Horizon – the universe is so uniform; ● Flatness – the universe is so old; ● Primordial perturbations – what is their origin;

9. ● Horizon – the universe is so uniform; ● Flatness – the universe is so old; ● Horizon – the universe is so uniform; ● Flatness – the universe is so old; Inflation ==> Inflation: ll <== / ll <== / ● Primordial perturbations – what is their origin;

10. Superhorizon Density perturbations ● Perturbations are superhorizon ● One can mimic acoustic peaks… ● … but not superhorizon correlations; ● Perturbations are superhorizon ● One can mimic acoustic peaks… ● … but not superhorizon correlations; Hu et al. (1997) TE cross correlation Barreiro (2009) ● => Inflation

11. 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. ● 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.

12. ● Curvature perturbations – random fields ; ● Isotropic two point correlation function: isotropic => ● Momentum space: ● Curvature perturbations – random fields ; ● Isotropic two point correlation function: isotropic => ● Momentum space: Random Fields

13. ● Two point correlator in momentum space: ● The shape of the power spectrum: ● Inflation models => ● WMAP 5yr measurements: ● Errorbars small enough to rule out some inflationary models ● Two point correlator in momentum space: ● The shape of the power spectrum: ● Inflation models => ● WMAP 5yr measurements: ● Errorbars small enough to rule out some inflationary models Correlation function

14. ● Three point correlator: ● Non-Gaussianity parameter: ● Single field inflation => Gaussian perturbations: ● WMAP 5yr measurements: ● Three point correlator: ● Non-Gaussianity parameter: ● Single field inflation => Gaussian perturbations: ● WMAP 5yr measurements: Higher Order Correlators

15. Statistical Anisotropy ● New observable; ● Anisotropic two point correlation function ● Anisotropic if for ● The anisotropic power spectrum: ● The anisotropic bispectrum: ● New observable; ● Anisotropic two point correlation function ● Anisotropic if for ● The anisotropic power spectrum: ● The anisotropic bispectrum:

16. Random Fields with Statistical Anisotropy Isotropic - preferred direction

17. Vector Field Model ● Until recently only scalar fields were considered for production of primordial curvature perturbations; ● We consider curvature perturbations from vector fields; ● Until recently only scalar fields were considered for production of primordial curvature perturbations; ● We consider curvature perturbations from vector fields;

18. 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 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;

19. 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 ● The energy momentum tensor: I.Inflation II.Light Vector Field III.Heavy Vector Field IV.Vector Field Decay. Onset of Hot Big Bang

20. 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 ● 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

21. Power Spectra

22. Anisotropic Perturbations ● Curvature perturbations statistically anisotropic; =>Vector contribution subdominant ● Non-Gaussianity: ● Correlated with statistical anisotropy ● Itself anisotropic ● Smoking gun for the vector field contribution to the curvature perturbations. ● Curvature perturbations statistically anisotropic; =>Vector contribution subdominant ● Non-Gaussianity: ● Correlated with statistical anisotropy ● Itself anisotropic ● Smoking gun for the vector field contribution to the curvature perturbations. Groeneboom et al. (2009)

23. 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: ● 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:

24. 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; ● 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;