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

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

7-year WMAP 2010

PR(k)= (δρ/ρ)2

Running spectral index

Inflation and Primordial Density Fluctuations

H

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

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

Large-scale CMB anomalies

WMAP1 WMAP3 Low quadrupole

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)

WMAP3 CMB sky map

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

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

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

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

Start of inflation

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

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

Following is an effort to go from homogenous to directional effects

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

Inflaton fluctuations Expansion parameter where the source term

Solutions Zero order First order

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

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

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…

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

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

Motion of the bubble wall surface tension bubble radius

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

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