Towards Constraining the initial state using Non-Gaussianities Daan Meerburg University of...
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Transcript of Towards Constraining the initial state using Non-Gaussianities Daan Meerburg University of...
Towards Constraining the initial state using Non-GaussianitiesDaan Meerburg
University of Amsterdam, ITF-API
PASCOS 2008
WORK IN PROGRESS: Meerburg and van der Schaar
MAIN MESSAGE
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Initial state modifications always lead to enfolded non-Gaussianities
(NG)
BEFT gives extra contribution ((cor)related) [WIP]
Construction of enfolded template
Bounding enfolded NG might strongly constrain the initial state
OUTLINE
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Introduction
BEFT(Boundary Effective Field Theory)
Non-Gaussianities
Conclusions
Non-Gaussian Shapes
INTRODUCTION
Komatsu et al. 2002PASCOS 2008
INTRODUCTION
> Degrees of Freedom
Deviation from Random
Quantum fl. -> Inflation
Different Models, Different ShapesSignature of Fundamental Physics
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BEFT2 Possibilities to set a
BoundaryNPH BEFT
Schalm, Shiu & v d Schaar 2005
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Danielsson 2002
BEFT
In the language of Actions:
For single field models
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BEFT
The idea:
Tolley & Holman 2007, Porrati 2005
Computing prim. 3p functionNeed to consider:
1) 3pf from boundary:
2) 3pf from bulk:
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BEFT
Using the in-in formalism
Schwinger 1961, Keldysh 1964
where
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Contribution from Bulk (SFSR)
NON-GAUSSIANITIES
With
PASCOS 2008 Holman & Tolley 2007
Contribution from Bulk (SFSR)
NON-GAUSSIANITIES
With
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Max:
ENFOLDED!
NON-GAUSSIANITIESContribution from Boundary (WIP):
Poratti et al 2005, Meerburg & v d Schaar
With
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Vanishes for modes , working on details of what happens in between.
For super-horizon modes ( ) :
LOCAL!
NON-GAUSSIAN SHAPES
Non-Gaussian Shapes
Komatsu et al, Babich, Creminelli 2004
Local, Equilateral & Enfolded
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NON-GAUSSIAN SHAPES
Factorizable template
Take and replace and demand
PASCOS 2008 Meerburg & v d Schaar in prep.
NON-GAUSSIAN SHAPES
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NON-GAUSSIAN SHAPES
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Three templates, three extremeTriangles:
Last triangle seem to be unique forInitial state mod.
Equilateral and local shape alone do not completely
parameterize a general 3p function
NON-GAUSSIAN SHAPES
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Example: ‘Flat shape’
Can be written as:
When this shape dominates data then:
CONCLUSIONS
BEFT elegant approach to take all contributions due to initial state mod. in consideration
Non-Gaussianities coming from bulk and boundary differ: shapes, regimeand likely amplitude (WIP)
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Measure using our template to constrain initial state
HYPOTHETICAL CONSTRAINTS
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From bulk
If:
Then
WIPStill need to relate to . Basically comparing a Gaussian to a Non-Gaussian, using one parameter
Constrain in CMB data, as done for and
Consider higher order correlation function in part. for boundary action
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Do these triangles represent a fullset?