1. Inflation after WMAP Kin-Wang Ng (吳建宏) Academia Sinica, Taiwan
2nd International Workshop on
Dark Matter, Dark Energy, and
Matter-Antimatter Asymmetry
Hsinchu, Nov 5 – 6 , 2010
Collaborators: Yeo-Yie Charng, Hing-Tong Cho, Da-Shin Lee, Wolung Lee,
I-Chin Wang, Chun-Hsien Wu

2. Outline Cosmic background backgroud anisotropy and WMAP observation
Primordial density perturbation
scale-invariant, running spectral index, Gaussianity
Large-scale CMB anomalies
Implications to inflation

4. 7-year
WMAP 2010

5. PR(k)= (δρ/ρ)2

6. Running
spectral
index

7. Inflation and Primordial Density Fluctuations

8. H

9. |dn/dlnk| << |n-1|
PR(k)= (δρ/ρ)2
|dn/dlnk| << |n-1|

10. Radiation transfer function
Curvature potential
▽2Φ=δρ/ρ
Slow-roll inflation
WMAP3 Data on Non-Gaussianity
Radiation transfer function

11. Large-scale CMB anomalies

12. WMAP1
WMAP3
Low quadrupole

13. South-North Power Asymmetry
Eriksen et al 04
Park 04
South-North Power Asymmetry
Eriksen et al 04
northern hemisphere
southern hemisphere
full sky
North pole (80o,57o)

14. WMAP3
CMB sky map

15. “Axis of Evil”
Land & Magueijo 05
l=2, quadrupole
l=3, octopole

16. A Challenge to Standard Slow-roll inflation!?
Slow-roll kinematics
Quantum fluctuations
Chaotic inflation – classical fluctuations driven by a white noise (Starobinsky) or by a colored noise (Liguori, Matarrese et al.) coming from high-k inflaton
Driven by a colored noise from interacting quantum environment (Wu et al)
Trapped inflation (Green et al)
Slow-roll conditions violated after horizon crossing (Leach et al)
General slow-roll condition (Steward)
|n-1|~|dn/dlnk|
Multi-field (Vernizzi, Tent, Rigopoulos, Yokoyama et al)
etc

17. Our Inflaton-Scalar Interacting Model
(Wu et al 07)
Single-field inflation〈σ〉= 0

18. Trace out sigma field to obtain :
Feynman & Vernon 1963
Influence Functional Method
Colored, dependent on history
Dissipation
Noise
imaginary part
real part
semi-classical

21. Start of inflation

22. Dominant passive fluctuations and low CMB quadrupole
assuming no active de Sitter quantum fluctuations

23. Running spectral index and Non-gaussianity
We propose a new dynamical source for density perturbation: Colored Quantum Noise
- give a low CMB quadrupole
Can be applied to trapped inflation (Green et al. 09)
Working on running spectral index and non-Gaussianity, both are natural with colored noise ns
Dissipation?
Relative large
three-point functions

24. Following is an effort to go from homogenous to directional effects

25. A black hole in inflation Cho, Ng, Wang 09
M - black hole mass
H - Hubble parameter
Schwarzschild-de Sitter
Static > Planar

26. Inflaton
fluctuations
Expansion
parameter
where the source term

27. Solutions
Zero order
First order

28. Power spectrum
de Sitter
quantum fluctuations
End of inflation  → 0

29. Possible effects to CMB anisotropy
Inflation
present universe
early universe
e.g. black holes
formed via
thermal
fluctuations
Scardigli et al.
Carroll, Tseng, & Wise 08 preferred point, line, or plane

30. Speculations
Is it possible not to fine tune inflation duration to 60 efolds?
Then there must be something taking place during slow-roll inflation
Formation rate must not be far below the expansion rate of inflation
e.g. Collapse of density peaks of quantum fluctuations during inflation or…

31. String Landscape 10500 de Sitter vacua
Metastable, bubble nucleation via tunneling
Barriers of string scale, slow tunneling rate
The spacetime is a hierachy of de Sitter vacuum bubbles
Most part in eternal inflation
Some regions tunnel down to flat potential for slow-roll infaltion
We sit in a vacuum with a small cosmological constant today

32. Efficient and rapid tunneling
Tye, Shiu,…
slow-roll inflation in a de Sitter vauum Λ2
Will these bubbles Λ1 collapse
into black holes? Λ2 Λ1

33. Motion of the bubble wall
surface
tension
bubble radius

34. Work is in progress towards an explanation of large-scale CMB anomalies with black holes, domain filaments, and bubble walls

35. Conclusion
Hints from WMAP data on beyond standard slow-roll inflation !?
A fine tuning – physics just at 60 e-foldings
Maybe there is a window to see the first few e-foldings of inflation !?
Many models give a suppressed CMB low multipoles and/or directional effects
Perhaps we are all fooled by probability – it is indeed a Gaussian quantum process
Nongaussianity is an important check