anisotropic non gaussianity
Skip this Video
Download Presentation
Anisotropic non-Gaussianity

Loading in 2 Seconds...

play fullscreen
1 / 18

Anisotropic non-Gaussianity - PowerPoint PPT Presentation

  • Uploaded on

Anisotropic non-Gaussianity. Mindaugas Karčiauskas work done with Konstantinos Dimopoulos David H. Lyth. arXiv: 0812.0264. Density perturbations. Primordial curvature perturbation – a unique window to the early universe; Origin of structure <= quantum fluctuations;

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Anisotropic non-Gaussianity' - osmond

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
anisotropic non gaussianity

Anisotropic non-Gaussianity

Mindaugas Karčiauskas

work done with

Konstantinos Dimopoulos

David H. Lyth


density perturbations
Density perturbations
  • Primordial curvature perturbation – a unique window to the early universe;
  • Origin of structure <= quantum fluctuations;
  • Usually light, canonically normalized scalar fields => statistical homogeneity and isotropy;
  • Statistically anisotropic perturbations from the vacuum with a broken rotational symmetry;
  • The resulting is anisotropic and may be observable.
statistical homogeneity and isotropy
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;
statistical homogeneity and isotropy1
Statistical homogeneity and isotropy
  • Assume statistical homogeneity;
  • Two point correlation function
    • Isotropic if for ;
  • The isotropic power spectrum:
  • The isotropic bispectrum:
statistical homogeneity and isotropy2
Statistical homogeneity and isotropy
  • Two point correlation function
    • Anisotropic if even for ;
  • The anisotropic power spectrum:
  • The anisotropic bispectrum:
random fields with statistical anisotropy
Random Fields with Statistical Anisotropy


- preferred direction

present observational constrains
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.
origin of statistically anisotropic power spectrum
Origin of Statistically Anisotropic Power Spectrum
  • Homogeneous and isotropic vacuum => the statistically isotropic perturbation;
  • For the statistically anisotropic perturbation <= a vacuum with broken rotational symmetry;
  • Vector fields with non-zero expectation value;
  • Particle production => conformal invariance of massless U(1) vector fields must be broken;
  • We calculate for two examples:
    • End-of-inflation scenario;
    • Vector curvaton model.
n formalism
δN 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.

end of inflation scenario basic idea1
End-of-Inflation Scenario: Basic Idea

- light scalar field.


Statistical Anisotropy at the End-of-Inflation Scenario
  • Physical vector field:
  • Non-canonical kinetic function ;
  • Scale invariant power spectrum => ;
  • Only the subdominant contribution;
  • Non-Gaussianity:

where , - slow roll parameter

curvaton mechanism basic idea



Curvaton Mechanism: Basic Idea
  • Curvaton (Lyth, Wands (2002); Enquist, Sloth (2002)):
    • light scalar field;
    • does not drive inflation.
vector curvaton
Vector Curvaton
  • Vector field acts as the curvaton field (Dimopoulos (2006));
  • Only a smallcontribution to the perturbations generated during inflation;
  • Assuming:
    • scale invariant perturbation spectra;
    • no parity braking terms;
  • Non-Gaussianity:


estimation of
Estimation of  
  • In principle isotropic perturbations are possible from vector fields;
  • In general power spectra will be anisotropic => 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
  • 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 => smoking gun for vector field contribution to the curvature perturbation.