Anisotropic non-Gaussianity

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Anisotropic non-Gaussianity
arXiv0812.0264

• Mindaugas Karciauskas
• work done with
• Konstantinos Dimopoulos
• David H. Lyth

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Density perturbations

• Primordial curvature perturbation a unique
  window to the early universe
• Origin of structure lt quantum fluctuations
• Usually light, canonically normalized scalar
  fields gt statistical homogeneity and isotropy
• Statistically anisotropic perturbations from the
  vacuum with a broken rotational symmetry
• The resulting is anisotropic and may be
  observable.

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Statistical homogeneity and isotropy

• Density perturbations random fields
• Density contrast
• Multipoint probability distribution function
  
• Homogeneous if the same under translations of all
  
• Isotropic if the same under spatial rotation

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Statistical homogeneity and isotropy

• Assume statistical homogeneity
• Two point correlation function
• Isotropic if
  for
• The isotropic power spectrum
• The isotropic bispectrum

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Statistical homogeneity and isotropy

• Two point correlation function
• Anisotropic if even for
  
• The anisotropic power spectrum
• The anisotropic bispectrum

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Random Fields with Statistical Anisotropy
Isotropic
- preferred direction
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Present Observational Constrains

• The power spectrum of the curvature perturbation
  
• 
  almost scale invariant
• Non-Gaussianity from WMAP5 (Komatsu et. al.
  (2008))
• No tight constraints on anisotropic contribution
  yet
• Anisotropic power spectrum can be parametrized as
  
• Present bound (Groeneboom, Eriksen
  (2008))
• We have calculated of the anisotropic
  curvature perturbation - new observable.

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Origin of Statistically Anisotropic Power Spectrum

• Homogeneous and isotropic vacuum gt the
  statistically isotropic perturbation
• For the statistically anisotropic perturbation lt
  a vacuum with broken rotational symmetry
• Vector fields with non-zero expectation value
• Particle production gt conformal invariance of
  massless U(1) vector fields must be broken
• We calculate for two examples
• End-of-inflation scenario
• Vector curvaton model.

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dN formalism

• To calculate we use formalism
• (Sasaki, Stewart (1996) Lyth, Malik,
  Sasaki (2005))
• Recently in was generalized to include vector
  field perturbations (Dimopoulos, Lyth, Rodriguez
  (2008))
• where , ,
  etc.

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End-of-Inflation Scenario Basic Idea
Linde(1990)
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End-of-Inflation Scenario Basic Idea

• - light scalar field.

Lyth(2005)
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Statistical Anisotropy at the End-of-Inflation
Scenario

• - vector field.

Yokoyama, Soda (2008)
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Statistical Anisotropy at the End-of-Inflation
Scenario

• Physical vector field
• Non-canonical kinetic function
  
• Scale invariant power spectrum gt
• Only the subdominant contribution
• Non-Gaussianity
• where , - slow roll parameter

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Curvaton Mechanism Basic Idea

• Curvaton (Lyth, Wands (2002) Enquist, Sloth
  (2002))
• light scalar field
• does not drive inflation.

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Vector Curvaton

• Vector field acts as the curvaton field
  (Dimopoulos (2006))
• Only a small contribution to the perturbations
  generated during inflation
• Assuming
• scale invariant perturbation spectra
• no parity braking terms
• Non-Gaussianity

where
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Estimation of  

• In principle isotropic perturbations are possible
  from vector fields
• In general power spectra will be anisotropic gt
  must be subdominant ( )
• For subdominant contribution can be
  estimated on a fairly general grounds
• All calculations were done in the limit
  
• Assuming that one can show that

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Conclusions

• We considered anisotropic contribution to the
  power spectrum and
• calculated its non-Gaussianity parameter .
  
• We applied our formalism for two specific
  examples end-of-inflation and vector curvaton.
• . is anisotropic and correlated with the
  amount and direction of the anisotropy.
• The produced non-Gaussianity can be observable
• Our formalism can be easily applied to other
  known scenarios.
• If anisotropic is detected gt smoking gun
  for vector field contribution to the curvature
  perturbation.

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