Wilkinson Microwave Anisotropy Probe (WMAP) Observations: The Final Results

(1)

Wilkinson Microwave Anisotropy Probe (WMAP) Observations:

The Final Results

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

1

WMAP

(2)

WMAP at Lagrange 2 (L2) Point

June 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

2

used to be

September 8, 2010:

WMAP left L2

December 21, 2012:

The final, nine-year data release

(3)

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

3

(4)

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

4

(5)

WMAP9

+ACT+SPT WMAP9

+ACT+SPT +BAO+H0

5

(6)

Bispectrum Results

• ^f

^NL^local

= 37±20 (68% CL)

• after subtracting off the low-redshift ISW-lensing bias of Δ f

NLlocal

=2.6

• ^f

^NLequilateral

= 51±136 (68% CL)

• ^f

^NL^orthogonal

= –245±100 (68% CL)

• more later!

₆

We do not claim detection of any forms of non-Gaussianity k1

k2

k3

(7)

7

Helium Abundance by Mass Fraction 2

Effective Number of Relativistic Degrees of Freedom at z~1090

WMAP9

+ACT+SPT BBN prediction

(8)

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}

8

(9)

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

9

(10)

From “Cosmic Voyage”

(11)

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

(12)

(13)

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

13

θ

COBE

WMAP

(14)

COBE/DMR Power Spectrum Angle ~ 180 deg / l

Angular Wavenumber, l ¹⁴

~9 deg

~90 deg

(quadrupole)

(15)

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?

15

θ

COBE

WMAP

θ

(16)

WMAP 9-year Power Spectrum

Angular Power Spectrum

Large Scale Small Scale

about

1 degree on the sky COBE

16

(17)

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

(18)

9-year temperature C l

18

(19)

7-year temperature C l

19

(20)

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

(21)

Variance (sub-optimal) / Variance (optimal)

21

(22)

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

22

(23)

23

(24)

Adding the small-scale CMB data

•

Atacama Cosmology Telescope (ACT)

•

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

•

^C^l from Das et al. (2011)

•

South Pole Telescope (SPT)

•

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

•

^C^l 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]

24

(25)

South Pole Telescope (SPT)

Atacama Cosmology Telescope (ACT)

25

1000

100

(26)

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

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

26

(27)

The number of “neutrino” species

total radiation density:

photon density:

neutrino density:

neutrino+extra species:

where

27

(28)

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.

28

(29)

“Neutrinos” have anisotropic stress

•

This changes metric perturbations as 0-0

tr(i-j)

•

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

29

(30)

30

(31)

31

(32)

32

(33)

33

(34)

34

(35)

Effect of helium on C l TT

•

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/(σ_Tne) = Enhanced Silk damping

35

(36)

36

(37)

37

(38)

Helium Abundance by Mass Fraction 38

Effective Number of Relativistic Degrees of Freedom at z~1090

WMAP9

+ACT+SPT

Simultaneous Fit to

Helium and N eff

Results consistent with the BBN prediction

BBN prediction

(39)

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?

39

(40)

WMAP 9-year Power Spectrum

about

1 degree on the sky COBE

40

(41)

Getting rid of the Sound Waves

41

Primordial Ripples

(42)

The Early Universe Could Have Done This Instead

42

More Power on Large Scales

Small Scale Large Scale

(43)

...or, This.

43

More Power on Small Scales

(44)

...or, This.

44

Parametrization:

l(l+1)C l ~ l ^ns–1

And, inflation predicts n s ~1

(45)

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

• Gravitational waves stretch

space, causing particles to move.

45

(46)

Two Polarization States of GW

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

46

(47)

From GW to CMB Anisotropy

47

(48)

From GW to CMB Anisotropy

48

Redshift

Blueshift Blueshift

Redshift

Blues Blues hift

hift

(49)

“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

49

(50)

WMAP9

+ACT+SPT WMAP9

50

(51)

What do “BAO” and “H 0 ” do?

•

^{BAO and H}⁰ 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

(52)

R ² Inflation [Starobinsky 1980]

•

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

where

52

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

(53)

Bispectrum

•

Three-point function!

•

^B^ζ^(k¹^,k²^,k³⁾

= <ζ_k1ζ_k2ζ_k3> = (amplitude) x (2π)³δ(k₁+k2+k3)F(k1,k2,k3)

53

model-dependent function

k1

k2

k3

Primordial fluctuation ”fNL”

(54)

MOST IMPORTANT

(55)

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:

•

^f^NL = 37 ± 20 (1σ)

•

The WMAP data are consistent with the prediction of

simple single-field inflation models: 1–ns≈r≈fNL ₅₅

(56)

Komatsu&Spergel (2001)

56

(57)

57

(58)

FIELD INTERACTION

• ^f

^NLequilateral

= 51±136 (68% CL)

• no evidence whatsoever

58

(59)

“Orthogonal” Shape

•

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

59

(60)

“Orthogonal” Shape

•

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

60

• ^f

^NL^orthogonal

= –245±100 (68% CL)

• Statistically, it is a 2.45 σ 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.

(61)

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!

61

(62)

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

62

(63)

63

(64)

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.

64

(65)

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.

65

(66)

•

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

Normal Map

66

(67)

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)

67

(68)

Trispectrum

•

^T^ζ^(k¹^,k²^,k³^,k⁴^)=(2π)³^δ(k¹^+k²^+k³^+k⁴⁾

{gNL[(54/25)Pζ(k1)Pζ(k2)Pζ(k3)+cyc.]

+τ_NL[Pζ(k1)Pζ(k2)(Pζ(|k1+k3|)+Pζ(|k1+k4|))+cyc.]}

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

multi-field inflation!

k3

k4

k2

k1

g NL

k2

k1

k3

k4

τ _NL

⁶⁸

(69)

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.

ln(fNL) 69

ln(τ_NL)

77 3.3x10⁴

(Smidt et al. 2010)

(70)

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(τ_NL)

10 600

70

(71)

Case B: Multi-field Happiness

•

^f^NL is detected. Single- field is dead.

•

^{But, τ}^NL^{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(τ_NL)

600

30 71

(72)

Case C: Madness

•

^f^NL is detected. Single- field is dead.

•

^{But, τ}^NL^{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(τ_NL)

30 600

72

Wilkinson Microwave Anisotropy Probe (WMAP) Observations: The Final Results