position space cmb anomalies from multi-stream...

Position space CMB anomalies from

multi-stream inflation

Yi Wang, IPMU, May 2013

Outline:

∙ Cosmology after Planck

- standard model, extensions and anomalies

∙ Multi-stream inflation

- the model

- hemispherical power asymmetry

- the cold spot

- low � suppression, multipole alignment

- constraining multi-field inflation

Cosmology after Planck

Planck:

∙ Collecting data since 2009

∙ Data release: 21 Mar, 2013

The 6-parameter standard model works well:

∙ Background:

h = 67.11, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)

∙ Initial perturbations:

Aζ = 2.215 × 10-9 , ns = 0.962

∙ Reionization history: τ = 0.0925


∙ Background:

h = 67.11, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.96


h was 71.2 for WMAP+SPT+ACT+SNLS3

As a result, t is now 13.8 Gyr (13.7 before).₀

↓


∙ Background:

h = 67.11, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.962



∙ Background:

h = 67.11, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.96


↓

ΩΛ was 0.736 for WMAP+SPT+ACT+SNLS3


∙ Background:

H = 0.6711, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.962



∙ Background:

h = 67.11, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.96


Almost unchanged.

But h decreased thus Ωb and Ωc are now 10% greater


∙ Background:

H = 0.6711, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.962



∙ Background:

h = 67.11, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.96


↓

Aζ was 2.407 × 10-9 for WMAP+SPT+ACT+SNLS3


∙ Background:

H = 0.6711, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.962



∙ Background:

h = 67.11, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.962

∙ Reionization history: τ = 0.0925ns was 0.967 for WMAP+SPT+ACT+SNLS3

ns<1: previously 5σ (WMAP9+BAO), now at 5.4σ.

↓


∙ Background:

H = 0.6711, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.962



∙ Background:

h = 67.11, ΩΛ = 0.68, Ωbh² = 0.022, Ωch² = 0.12

(Ωb+Ωc+ΩΛ = 1)


Aζ = 2.215 × 10-9 , ns = 0.962

∙ Reionization history: τ = 0.0925 ↑

τ was 0.086 for WMAP+SPT+ACT+SNLS3

But error bar is 0.03ish,

Planck + WP central value agrees with WMAP

One parameter extensions: (95% CL)

∙ Spatial curvature: -0.0371 < Ωk < 0.0060

∙ Neutrino Σmν < 0.230eV, 2.79 < neff < 3.84

∙ Tensor to scalar ration: r < 0.111,

∙ Running of spetial index: -0.031 < αs < 0.002

∙ EoS of dark energy: -1.38 < w < -0.93

∙ Non-Gaussianities:

local: -8.9 < fNL < 14.3,

equil: -192 < fNL < 108, ortho: -103 < fNL < 53







∙ Non-Gaussianities: (low � agree with WMAP)

local: -8.9 < fNL < 14.3,


Currently Planck polarization not yet used.

c.f. r<0.13 (95% CL) for WMAP9 + SPT + ACT + BAO + H0

Green: WMAP9 + SPT + ACT

Red: WMAP9 + SPT + ACT + BAO + H0





∙ Running of spectral index: -0.031 < αs < 0.002



local: -8.9 < fNL < 14.3,









local: -8.9 < fNL < 14.3,


WMAP9:

local: -3 < fNL < 77,

equil: -221 < fNL < 323, ortho: -445 < fNL < -45

Interestingly, Planck agrees with WMAP at low �

Planck 2013 on Quasi-single field non-G (C. Chen & YW, 2009)c.f. “Planck-Suppressed Operators,” Assassi, Baumann, Green, McAllister, 2013

Anomalies – overview

L. Page

Anomalies – overview

∙ Hemispherical asym (Eriksen, et. al. 2003)

∙ Dipolar asymmetry (Gordon et. al. 2005)

∙ Cold spot (Vielva et. al. 2003)

∙ Mode alignment (Tegmark et. al. 2003)

∙ Power suppression at low multipoles (WMAP, Planck)

∙ Parity asymmetry, phase correlations, ...

Anomalies – asymmetry

∙ Hemispherical asymmetry

Asymmetry between two hemispheres

∙ Dipolar asymmetry

Asymmetry characterized by a dipole

A(n) = (1 + w ∙ n) A0

∙ They are related but different effects

See, e. g. WMAP 7

From Planck website (anomalous regions enhanced, caption was wrong)

Hemispherical: directions (Planck 2013)

High � directions

Small � directions

Hemispherical: amplitude difference (Planck 2013)

Anomalies – asymmetry

Hemispherical asymmetry v.s. Dipolar asymmetry

For small �, say < 100: both ~ 10% modulation�For large �, say � > 100: Only hemispherical asym

(and direction then points to dipole direction)

There is a tension at � > 100.

Anomalies – cold spot

∙ About 5 degree² with 70µK colder than average

∙ More than 4σ unlikely from statistics


Different masks and CL (Planck 2013):

Alignment (axis of evil)

(Planck 2013)

9◦, 98%; or 13◦, 96.7%

(WMAP 7 was 3◦)

Quadrupole

Octopole

+: Quadrupole direction

*: Octopole direction

Low suppression (Planck 2013)�A power deficit of 5%~10% at ≤ 40, 2.5σ ~ 3σ�

multipole moment �

Multi-stream inflation

M. Li and YW, 0903.2123

S. Li, Y. Liu, Y. Piao, 0906.3608; YW, 1001.0008

N. Afshordi, A. Slosar, YW, 1006.5021

F. Duplessis, YW, R. Brandenberger, 1201.0029

YW, 1304.0599

Multi-stream inflation

Examples include:

Distance of rolling

EoM

Asymmetries

Cold spot:

a) Sachs-Wolfe

b) ISW, etc.

Constraint on multi-field potential

Temporary domain wall

Wang, Cho, Wu 2010, Wang, Wu, Hsu, 2011

In the locally de Sitter frame:

Observations are made in the domain wall rest frame

Domain wall induced power asymmetry

Probability of multipole directions

Probability of (3D) alignment

Future directions:

∙ In-in formalism for non-unique classical traj.

∙ Full grav. pert. with domain wall

∙ Beyond planar domain wall

∙ Time dependence of the domain wall tension

∙ Project the 3D alignment prob. to 2D

∙ Fitting multi-stream inflation with data

∙ Multiple dimensional random potential

Thank you!

position space cmb anomalies from multi-stream...

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