بسم الله الرحمن الرحیمphysics.ipm.ac.ir/courses/pdfseminar1/namjoo1.pdf ·...
Transcript of بسم الله الرحمن الرحیمphysics.ipm.ac.ir/courses/pdfseminar1/namjoo1.pdf ·...
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Non-Gaussianity
Mohammad Hossein Namjoo
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Outline Inflation Observational cosmology Theoretical cosmology Non-Gaussianity and its
charcteristics
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Standard Modelof Cosmology
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Problems of standard model
Flatness problem
Horizon problem
Monopole problem
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Solving the problems:Inflation
Accelerating universe can solve the problems.A.Guth 1980
Solution to: Flatness problem Horizon problem Monopoles problem
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Dynamics of Inflation
)3(34
2 Pma
a
P
+−= ρπ
2 22
8( )P
aHa m
π ρ= =
Friedmannequations Accelerating the
universe needs extraordinary content
• Matter content of universe at inflationary phase is inflaton, a scalar field
• Accelerating is possible:
)(21,)(
21 22 φφφφρ φφ VPV −=+=
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conditions for inflation: Slow-Roll conditions:
• In order to inflation occurs and lasts sufficiently long time.
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B.~A.~Bassett, S.~Tsujikawa and D.~Wands, %``Inflation dynamics and reheating,''Rev.\ Mod.\ Phys.\ \ {\bf 78}, 537 (2006)[astro-ph/0507632].
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CMB: The observationsCMB: Radio waves remained from early universe.We observe them when they reach to our horizon.
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Today/Future observations
WMAP,7th year
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What we learn from CMB data?
Power spectrum: The relation between CMB anisotropy and quantum fluctuationsof early universe
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Non-Gaussianity:Measures the correlation between different scales or different parts of the universe.
Gaussian perturbations have zero non-Gaussianity
What we learn from CMB data?
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Quantum fluctuations exist naturally
Can they be the initial seeds of CMB fluctuations?
How can we build fluctuations on CMB?
Inflation can do that
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How can we model the CMB? Perturbation theory in cosmology
Perturbation of metric around FRW background:
+ Perturbation of matter:
A good quantity!
Curvature perturbation:
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Power spectrum/non-Gaussianityand CMB
Power spectrum of curvature perturbation:
Non-Gaussianity:
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To gather… Inflation Observation of temperature fluctuations Cosmological perturbation theory and inflation Power spectrum and non-Gaussianity
http://en.citizendium.org/wiki/File:060915_CMB_Timeline75.jpg
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Why non-Gaussianity is important?
Includes information about statistics of fluctuations
Can constrain or rule out models of inflation
Is both detectable and calculable (in principle)
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Characteristics of Non-Gaussianity
Size
Shape
Sign
These characteristics are detectable distinguishable
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http://www.umich.edu/~mctp/SciPrgPgs/events/2011/CosmoNongaussianity/index.html (by Matarrese)
Shape of Non-Gaussianity
Shape is the scale dependence of non-Gaussianity
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Size of Non-Gaussianity
http://www.umich.edu/~mctp/SciPrgPgs/events/2011/CosmoNongaussianity/index.html
Planck will have more to say about non-Gaussianity
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http://ipht.cea.fr/Pisp/pontavignon2008/programme.htm (by Wandelt & Yadav)
Is the non-Gaussianity large?
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How to calcualte the non-Gaussianity?
Maldacena’s Method
ᵟN formalism
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Maldacena’s method
%``Primordial non-Gaussianities in single field inflation,''JCAP\ {\bf 0506}, 003 (2005)[astro-ph/0503692].
Quadratic action(The propagator):
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Maldacena’s method Cubic action(The interaction):
%``Primordial non-Gaussianities in single field inflation,''JCAP\ {\bf 0506}, 003 (2005)[astro-ph/0503692].
• coupling constants!
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ᵟ
D.~Wands, K.~A.~Malik, D.~H.~Lyth and A.~R.~Liddle, %``A New approach to the evolution of cosmological perturbations on large scales,''Phys.\ Rev.\ D\ {\bf 62}, 043527 (2000)[astro-ph/0003278].
N Formalism
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Typical slow-roll single field inflation:
The size of non-Gaussianity is of order of slow-roll parameters and
non-detectable.
Multiple field inflation:Entropic perturbations can induce large non-Gaussianity
Some Examples
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Some Examples Dirac-Born-Infield (DBI) inflation:
Non-standard kinetic term
Non-trivial sound speed is responsible for large non-Gaussianity
M.~Alishahiha, E.~Silverstein and D.~Tong, %``DBI in the sky,''Phys.\ Rev.\ D\ {\bf 70}, 123505 (2004)[hep-th/0404084].
%``Primordial non-Gaussianities in single field inflation,''JCAP\ {\bf 0506}, 003 (2005)[astro-ph/0503692].
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Ghost inflation:The non-standard dispersion relation results large non-Gaussinaity
Some Examples N.~Arkani-Hamed, P.~Creminelli, S.~Mukohyama and M.~Zaldarriaga, %``Ghost inflation,''JCAP\ {\bf 0404}, 001 (2004)[hep-th/0312100].
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Conclusion
Non-Gaussianity is the three point correlation function of temperature fluctuations on CMB.
Different models predict different non-Gaussianity
The detection of size, shape and sign of Non-Gaussianity in forthcoming observations constrains models of inflation.
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Thank youمتشکرم
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