Primordial density perturbations from the vector fields

1
Primordial density perturbations from the vector
fields

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

2
Plan

• Hot Big Bang and its 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

4
The Universe After 1s

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

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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

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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

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The Universe After 1s

• Large Scale Structure formation
• Seed perturbations of theorder
• Subsequent growth due to gravitational
  instability

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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

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Inflation

• Horizon the universe is so uniform
• Flatness the universe is so old

gt Inflation
ll ll lt/

• Primordial perturbations what is their origin

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Superhorizon Density perturbations
TE cross correlation

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

Hu et al. (1997)

• gt Inflation

Barreiro (2009)
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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
  .

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Random Fields

• Curvature perturbations random fields
• Isotropic two point correlation function
• isotropic gt
• Momentum space

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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

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Higher Order Correlators

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

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Statistical Anisotropy

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

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Random Fields with Statistical Anisotropy
Isotropic
- preferred direction
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Vector Field Model

• Until recently only scalar fields were considered
  for production of primordial curvature
  perturbations
• We consider curvature perturbations from vector
  fields

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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

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Vector Curvaton Scenario

• The energy momentum tensor
• Inflation
• Light Vector Field
• Heavy Vector Field
• Vector Field Decay.Onset of Hot Big Bang

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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

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Power Spectra
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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)
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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

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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