Primordial density perturbations from the vector

fields

- Mindaugas Karciauskas
- in collaboration with
- Konstantinos Dimopoulos
- Jacques M. Wagstaff

Plan

- Hot Big Bang and its problems
- Primordial perturbations
- Inflation and CMB parameters
- New observable statistical anisotropy
- Vector curvaton model

The Universe After 1s

- The Universe is expanding
- Universe started being hot
- Big bang nucleosynthesis
- Large scale structure formation

The Universe After 1s

- The Universe is expanding
- Hubbles discovery 1929
- Current measurements
- Freedman et al. (2001)

The Universe After 1s

- The early universe was hot
- Discovery of the CMB
- A. Penzias R. Wilson (1965)
- Radiation which cooled downfrom 3000K to 2.7K
- Steady State Cosmology is wrong

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 observationsat

The Universe After 1s

- Large Scale Structure formation
- Seed perturbations of theorder
- 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

gt Inflation

ll ll lt/

- Primordial perturbations what is their origin

Superhorizon Density perturbations

TE cross correlation

- Perturbations are superhorizon
- One can mimic acousticpeaks
- but not superhorizoncorrelations

Hu et al. (1997)

- gt 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 gt
- Momentum space

Correlation function

- Two point correlator in momentum space
- The shape of thepower spectrum
- Inflation models gt
- WMAP 5yr measurements
- Errorbars small enough to rule out some

inflationary models

Higher Order Correlators

- Three point correlator
- Non-Gaussianity parameter
- Single field inflation gt Gaussian perturbations
- WMAP 5yr measurements

Statistical Anisotropy

- New observable
- Anisotropic two point correlation
- function
- Anisotropic if for
- The anisotropic power spectrum
- The anisotropic bispectrum

Random Fields with Statistical Anisotropy

Isotropic

- 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
- Conformaly invariant gt cannot undergo particle

production - Induces anisotropic expansion of the universe
- Brakes Lorentz invariance
- Solved by using massive vector field
- Conformal invariance is broken
- Oscillates and acts as pressureless isotropic

matter - Decays before BBN

Vector Curvaton Scenario

- The energy momentum tensor
- Inflation
- Light Vector Field
- Heavy Vector Field
- 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 gt scale invariant

perturbation spectra - At the end of inflation and

Power Spectra

Anisotropic Perturbations

- Curvature perturbations statistically

anisotropic - gt 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)

No Scalar Fields

- Curvature perturbations statistically isotropic
- gt 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