Wilkinson Microwave Anisotropy Probe (WMAP) Observations:

The Final ResultsEiichiro Komatsu (Max-Planck-Institut für Astrophysik)HEP-GR Colloquium, DAMTP, Cambridge, January 30, 2012

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WMAP

WMAP at Lagrange 2 (L2) PointJune 2001:

WMAP launched!

February 2003:The first-year data release

March 2006:The three-year data release

March 2008:The five-year data release

January 2010:The seven-year data release

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used to be

September 8, 2010:WMAP left L2

December 21, 2012:The final, nine-year data release

Why am I here?

• Why should HEP/GR people care about temperature and polarization maps of the sky measured in microwave bands?

• Because:

1. They tell us something about inflation in very high energy scale

2. They constrain physics beyond the SM: e.g., the effective number of relativistic degrees of freedom

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9-year Science Highlights

1. Single-field slow-roll inflation continues to be supported by the data, with much restricted range of the parameter space

2. The joint constraint on the helium abundance and the number of relativistic species from CMB strongly supports Big Bang nucleosynthesis

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WMAP9+ACT+SPT

WMAP9+ACT+SPT+BAO+H0

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Bispectrum Results• fNLlocal = 37±20 (68% CL)

• after subtracting off the low-redshift ISW-lensing bias of ΔfNLlocal=2.6

• fNLequilateral = 51±136 (68% CL)

• fNLorthogonal = –245±100 (68% CL)

• more later! 6

We do not claim detection of any forms of non-Gaussianity

k1

k2

k3

72Helium Abundance by Mass Fraction

Effe

ctiv

e N

umbe

r of

Rel

ativ

istic

Deg

rees

of

Fre

edom

at

z~10

90 WMAP9+ACT+SPT+BAO+H0

WMAP9+ACT+SPT

BBN prediction

WMAP Science Team

• C.L. Bennett

• G. Hinshaw

• N. Jarosik

• S.S. Meyer

• L. Page

• D.N. Spergel

• E.L. Wright

• M.R. Greason

• M. Halpern

• R.S. Hill

• A. Kogut

• M. Limon

• N. Odegard

• G.S. Tucker

• J. L.Weiland

• E.Wollack

• J. Dunkley

• B. Gold

• E. Komatsu

• D. Larson

• M.R. Nolta

• K.M. Smith

• C. Barnes

• R. Bean

• O. Dore

• H.V. Peiris

• L. Verde

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WMAP 9-Year Papers

• Bennett et al., “Final Maps and Results,” submitted to ApJS, arXiv:1212.5225

• Hinshaw et al., “Cosmological Parameter Results,” submitted to ApJS, arXiv:1212.5226

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From “Cosmic Voyage”

CMB: The Farthest and Oldest Light That We Can Ever Hope To Observe Directly

•When the Universe was 3000K (~380,000 years after the Big Bang), electrons and protons were combined to form neutral hydrogen. 11

Analysis: 2-point Correlation

• C(θ)=(1/4π)∑(2l+1)ClPl(cosθ)• How are temperatures on two

points on the sky, separated by θ, are correlated?

• “Power Spectrum,” Cl

– How much fluctuation power do we have at a given angular scale?

– l~180 degrees / θ

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θCOBE

WMAP

COBE/DMR Power SpectrumAngle ~ 180 deg / l

Angular Wavenumber, l14

~9 deg~90 deg(quadrupole)

COBE To WMAP

• COBE is unable to resolve the structures below ~7 degrees

• WMAP’s resolving power is 35 times better than COBE.

• What did WMAP see?

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θCOBE

WMAP

θ

WMAP 9-year Power SpectrumA

ngul

ar P

ower

Spe

ctru

m Large Scale Small Scale

about 1 degree

on the skyCOBE

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The Cosmic Sound Wave

• “The Universe as a Miso soup”

• Main Ingredients: protons, helium nuclei, electrons, photons

• We measure the composition of the Universe by analyzing the wave form of the cosmic sound waves. 17

9-year temperature Cl

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7-year temperature Cl

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What changed?• An improved analysis! The error bar decreased by more

than expected for the number of years (9 vs 7). Why?

• We now use the optimal (minimum variance) estimator of the angular power spectrum.

• Previously, we estimated Cl for low-l (l<600) and high-l (l>600) separately. No weighting for low-l and inverse-noise-weighting for high-l.

• This results in a sub-optimal estimator near l~600.

• We now use the optimal (S+N)–1 weighting.20

Vari

ance

(su

b-op

timal

) / V

aria

nce

(opt

imal

)

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9-year (sub-optimal) vs 9-year (optimal)

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Adding the small-scale CMB data

• Atacama Cosmology Telescope (ACT)

• a 6-m telescope in Chile, led by Lyman Page (Princeton)

• Cl from Das et al. (2011)

• South Pole Telescope (SPT)

• a 10-m telescope in South Pole, led by John Carlstrom (Chicago)

• Cl from Keisler et al. (2011); Reichardt et al. (2012)These data are not the latest [Story et al. (2012) for SPT; Das et al. (2013) for ACT]

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South Pole Telescope (SPT)

Atacama Cosmology Telescope(ACT)

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1000

100

Adding the small-scale CMB tends to prefer a lower power at high

multipoles than predicted by the WMAP-only fit (~1σ lower)

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The number of “neutrino” speciestotal radiation density:

photon density:

neutrino density:

neutrino+extra species:

where

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What the extra radiation species does

• Extra energy density increases the expansion rate at the decoupling epoch.

• Smaller sound horizon: peak shifts to the high l

• Large damping-scale-to-sound-horizon ratio, causing more Silk damping at high l

• Massless free-streaming particles have anisotropic stress, affecting modes which entered the horizon during radiation era.

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“Neutrinos” have anisotropic stress

• This changes metric perturbations as

0-0tr(i-j)

• This changes the early Integrated-Sachs-Wolfe effect (ISW)29

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Effect of helium on ClTT

• We measure the baryon number density, nb, from the 1st-to-2nd peak ratio.

• For a given nb, we can calculate the number density of electrons: ne=(1–Yp/2)nb.

• As helium recombined at z~1800, there were even fewer electrons at the decoupling epoch (z=1090): ne=(1–Yp)nb.

• More helium = Fewer electrons = Longer photon mean free path 1/(σTne) = Enhanced Silk damping

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38Helium Abundance by Mass Fraction

Effe

ctiv

e N

umbe

r of

Rel

ativ

istic

Deg

rees

of

Fre

edom

at

z~10

90 WMAP9+ACT+SPT+BAO+H0

WMAP9+ACT+SPT

Simultaneous Fit to

Helium and Neff

Results consistent with the BBN prediction

BBN prediction

Implications for Inflation

• Two-point function analysis: the tensor-to-scalar ratio, r, and the primordial spectral tilt, ns

• Three-point function analysis: are fluctuations consistent with Gaussian?

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WMAP 9-year Power SpectrumA

ngul

ar P

ower

Spe

ctru

m Large Scale Small Scale

about 1 degree

on the skyCOBE

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Getting rid of the Sound WavesA

ngul

ar P

ower

Spe

ctru

m

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Primordial Ripples

Large Scale Small Scale

The Early Universe Could Have Done This InsteadA

ngul

ar P

ower

Spe

ctru

m

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More Power on Large Scales

Small ScaleLarge Scale

...or, This.A

ngul

ar P

ower

Spe

ctru

m

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More Power on Small Scales

Small ScaleLarge Scale

...or, This.A

ngul

ar P

ower

Spe

ctru

m

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Small ScaleLarge Scale

Parametrization: l(l+1)Cl ~ lns–1

And, inflation predicts ns~1

Gravitational waves are coming toward you... What do you do?

•Gravitational waves stretch space, causing particles to move.

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Two Polarization States of GW

• This is great - this will automatically generate quadrupolar anisotropy!

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From GW to CMB Anisotropy

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From GW to CMB Anisotropy

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Redshift

Redshift

Blue

shift

Blue

shift

Redshift

RedshiftBlu

eshif

tBlues

hift

“Tensor-to-scalar Ratio,” r

r = [Power in Gravitational Waves]

/ [Power in Gravitational Potential]

Theory of “Cosmic Inflation” predicts r <~ 1– I will come back to this in a moment

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WMAP9+ACT+SPT

WMAP9+ACT+SPT+BAO+H0

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What do “BAO” and “H0” do?

• BAO and H0 both measure distances in a low-z universe. This helps determine the matter density independent of ns. (In the temperature power spectrum, there is a mild correlation between them.) 51

R2 Inflation [Starobinsky 1980]

• This theory is conformally equivalent to a theory with a canonically normalized scalar field with a potential given by

where

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[very flat potential for large Ψ –> smaller r]

Bispectrum

• Three-point function!

• Bζ(k1,k2,k3) = <ζk1ζk2ζk3> = (amplitude) x (2π)3δ(k1+k2+k3)F(k1,k2,k3)

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model-dependent function

k1

k2

k3

Primordial fluctuation ”fNL”

MOST IMPORTANT

Probing Inflation (3-point Function)• Inflation models predict that primordial fluctuations are very

close to Gaussian.

• In fact, ALL SINGLE-FIELD models predict a particular form of 3-point function to have the amplitude of fNL=0.02.

• Detection of fNL>1 would rule out ALL single-field models!

• No detection of 3-point functions of primordial curvature perturbations. The 68% CL limit is:

• fNL = 37 ± 20 (1σ)

• The WMAP data are consistent with the prediction of simple single-field inflation models: 1–ns≈r≈fNL 55

Komatsu&Spergel (2001)

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FIELD INTERACTION

• fNLequilateral = 51±136 (68% CL)

• no evidence whatsoever

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“Orthogonal” Shape

• It’s a tricky shape: negative in the folded limit; positive in the equilateral limit

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“Orthogonal” Shape

• It’s a tricky shape: negative in the folded limit; positive in the equilateral limit

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• fNLorthogonal = –245±100 (68% CL)

• Statistically, it is a 2.45σ result.

Don’t jump: we do not claim that this is a detection,

while this is an intriguing result. Now, look at the null tests.

A long story short:

• A channel-to-channel consistency test is a little bit worrying, but we did not find an obvious systematics which can make this signal go away. Wait for Planck!

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Statistical Anisotropy• Is the power spectrum anisotropic?

• P(k) = P(|k|)[1+g*(cosθ)2]

• This makes shapes of temperature spots anisotropic on the sky.

• Statistically significant detection of g*

• Is this cosmological?

• The answer is no: the same (identical!) effect can be caused by ellipticity of beams

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This is coupled with the scan pattern

• WMAP scans the ecliptic poles many more times and from different orientations.

• Thus, the averaged beam is nearly circular in the poles.

• The ecliptic plane is scanned less frequently and from limited orientations.

• Thus, the averaged beam is more elliptical in the plane.

• This is exactly what the anisotropic power spectrum gives.

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Creating a map with a circular beam

• We create a map in which the elliptical beam shape is deconvolved. The resulting map has an effective circular beam.

• This map is not used for cosmology, but used for the analysis of foregrounds and statistical anisotropy.

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• A deconvolved image of a supernova remnant “Tau A” at 23 GHz

• Deconvolved image is more circular, as expected

• Deconvolved map does not show the anisotropic power spectrum anymore!

-5 5

Beam Sym. Map Residuals

-5 5

Normal Map Residuals

0 100

Beam Sym. Map

0 100

mK

mK

mK

mK

Normal Map

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a”

Summary• The minimal, 6-parameter ΛCDM model continues to

describe all the data we have

• No significant deviation from the minimal model

• Rather stringent constraints on inflation models

• Strong support for Big Bang nucleosynthesis with the standard effective number of neutrino species

• Anisotropic power spectrum is due to elliptical beams

...“(Hinshaw et al. 2012)

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Trispectrum

• Tζ(k1,k2,k3,k4)=(2π)3δ(k1+k2+k3+k4) {gNL[(54/25)Pζ(k1)Pζ(k2)Pζ(k3)+cyc.] +τNL[Pζ(k1)Pζ(k2)(Pζ(|k1+k3|)+Pζ(|k1+k4|))+cyc.]}

The consistency relation, τNL≥(6/5)(fNL)2, may not be respected – additional test of

multi-field inflation!

k3

k4

k2

k1

gNL

k2

k1

k3

k4

τNL 68

The 4-point vs 3-point diagram

• The current limits from WMAP 9-year are consistent with single-field or multi-field models.

• So, let’s play around with the future.

69ln(fNL)

ln(τNL)

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3.3x104

(Smidt et al. 2010)

Case A: Single-field Happiness

• No detection of anything after Planck. Single-field survived the test (for the moment: the future galaxy surveys can improve the limits by a factor of ten).

ln(fNL)

ln(τNL)

10

600

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Case B: Multi-field Happiness• fNL is detected. Single-

field is dead.

• But, τNL is also detected, in accordance with the Suyama-Yamaguchi inequality, as expected from most (if not all - left unproven) of multi-field models.

ln(fNL)

ln(τNL)

600

7130

Case C: Madness• fNL is detected. Single-

field is dead.

• But, τNL is not detected, inconsistent with the Suyama-Yamaguchi inequality.

• (With the caveat that this may not be completely general) BOTH the single-field and multi-field are gone.ln(fNL)

ln(τNL)

30

600

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