Critical Tests of Theory of the Early Universe using the CMB

(1)

Critical Tests of Theory of the Early Universe using the CMB

Eiichiro Komatsu (MPA)

ESO Colloquium, January 17, 2013

1

WMAP

(2)

Cosmology: The Questions

•

How much do we understand our Universe?

•

How old is it?

•

How big is it?

•

What shape does it take?

•

What is it made of?

•

How did it begin?

2

(3)

The Breakthrough

•

Now we can observe the physical condition of the Universe when it was very young.

3

(4)

Cosmic Microwave Background (CMB)

•

Fossil light of the Big Bang!

4

(5)

From “Cosmic Voyage”

(6)

How was CMB created?

•

When the Universe was hot, it was a hot soup made of:

•

Protons, electrons, and helium nuclei

•

Photons and neutrinos

•

Dark matter (DM)

•

DM does not do much, except for providing a a gravitational potential because ρDM/ρH,He~5

6

(7)

Universe as a hot soup

•

Free electrons can scatter photons

efficiently.

•

Photons cannot go very far.

proton helium

electron

photon

7

(8)

Recombination and Decoupling

•

[recombination]

When the temperature falls below 3000 K,

almost all electrons are captured by protons

and helium nuclei.

•

[decoupling] Photons are no longer

scattered. I.e., photons and electrons are no

longer coupled.

Time

1500K

6000K

3000K

proton helium electron photon 8

(9)

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. ⁹

(10)

(11)

COBE/DMR, 1992

•Isotropic?

•CMB is anisotropic! (at the 1/100,000

level) ¹¹

Smoot et al. (1992)

1cm

6mm

3mm

(12)

WMAP WMAP Spacecraft Spacecraft

MAP990422

thermally isolated instrument cylinder

secondary reflectors

focal plane assembly feed horns

back to back Gregorian optics, 1.4 x 1.6 m primaries

upper omni antenna line of sight

deployed solar array w/ web shielding medium gain antennae

passive thermal radiator

warm spacecraft with:

- instrument electronics

- attitude control/propulsion - command/data handling - battery and power control

60K

90K

300K

Radiative Cooling: No Cryogenic System

12

(13)

COBE to WMAP (x35 better resolution)

COBE

WMAP

COBE 1989

WMAP

2001 ¹³

(14)

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

14

used to be

September 8, 2010:

WMAP left L2

December 21, 2012:

The final, nine-year data release

(15)

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}

15

(16)

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

16

(17)

23 GHz [unpolarized]

17

(18)

33 GHz [unpolarized]

18

(19)

41 GHz [unpolarized]

19

(20)

61 GHz [unpolarized]

20

(21)

94 GHz [unpolarized]

21

(22)

How many components?

1. CMB: Tν

~ ν

⁰

2. Synchrotron (electrons going around magnetic fields): Tν

~ ν

^–3

3. Free-free (electrons colliding with protons): Tν

~ ν

^–2

4. Dust (heated dust emitting thermal emission): Tν~ν² 5. Spinning dust (rapidly rotating tiny dust grains):

Tν~complicated

You need at least five frequencies to separate them! ₂₂

(23)

Galaxy-cleaned Map

23

(24)

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

24

θ

COBE

WMAP

(25)

COBE/DMR Power Spectrum Angle ~ 180 deg / l

Angular Wavenumber, l ²⁵

~9 deg

~90 deg

(quadrupole)

(26)

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?

26

θ

COBE

WMAP

θ

(27)

WMAP 9-year Power Spectrum

Angular Power Spectrum

Large Scale Small Scale

about

1 degree on the sky COBE

27

(28)

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. ²⁸

(29)

CMB to Baryon & Dark Matter

•

1-to-2: baryon-to-photon ratio

•

1-to-3: matter-to-radiation ratio Baryon Density (Ωb)

Total Matter Density (Ωm)

=Baryon+Dark Matter

29

(30)

Total Matter Density from z=1090

Total Energy Density from the Distance to z=1090

• Angular Diameter Distance to z=1090

=H

0–1

∫ dz / [Ω

_m

(1+z)

³

+ Ω

Λ

]

^1/2 ³⁰

Ω_m

dark energy

(31)

31

Dark Energy: 72.1%

Dark Matter: 23.3%

H&He: 4.6%

Age: 13.7 billion years H0: 70 km/s/Mpc

(32)

CMB Polarization

• CMB is (very weakly) polarized!

³²

(33)

“Stokes Parameters”

33

Q<0; U=0 North

East

(34)

23 GHz [polarized]

Stokes Q Stokes U

34

(35)

23 GHz [polarized]

Stokes Q Stokes U

North East

35

(36)

33 GHz [polarized]

Stokes Q Stokes U

36

(37)

41 GHz [polarized]

Stokes Q Stokes U

37

(38)

61 GHz [polarized]

Stokes Q Stokes U

38

(39)

94 GHz [polarized]

Stokes Q Stokes U

39

(40)

How many components?

1. CMB: Tν

~ ν

⁰

2. Synchrotron (electrons going around magnetic fields): Tν

~ ν

^–3

3. Free-free (electrons colliding with protons): Tν

~ ν

^–2

4. Dust (heated dust emitting thermal emission): Tν~ν² 5. Spinning dust (rapidly rotating tiny dust grains):

Tν~complicated

You need at least THREE frequencies to separate them! ₄₀

(41)

Physics of CMB Polarization

•

CMB Polarization is created by a local temperature

quadrupole anisotropy. ⁴¹

Wayne Hu

(42)

Stacking Analysis

• Stack polarization images around

temperature hot and cold spots.

• Outside of the Galaxy mask (not shown), there are 11536 hot spots and 11752 cold spots.

42

(43)

Radial and Tangential Polarization Patterns

around Temp. Spots

•

All hot and cold spots are stacked

•

“Compression phase” at θ=1.2 deg and

“slow-down phase” at θ=0.6 deg are predicted to be there and we observe them!

•

The 7-year overall significance level: 8σ

43

(44)

44

• The 9-year overall

significance level: 10 σ

(45)

E-mode and B-mode

•

Gravitational potential can generate the E-

mode polarization, but not B-modes.

•

Gravitational

waves can generate both E- and B-modes!

B mode

E mode

₄₅

(46)

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

• Gravitational waves stretch

space, causing particles to move.

46

(47)

Two Polarization States of GW

• This is great - this will automatically

generate quadrupolar anisotropy around electrons!

47

(48)

From GW to CMB Polarization

48

Electron

(49)

From GW to CMB Polarization

49

Redshift

Blueshift Blueshift

Redshift

Blues Blues hift

hift

(50)

From GW to CMB Polarization

50

Gravitational waves can produce

both E- and B-mode polarization

(51)

“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

51

(52)

•

No detection of B-mode polarization yet.

B-mode is the next holy grail!

Po la ri za tio n Po w er Spectrum

52

(53)

Theory of the Very Early Universe

•

The leading theoretical idea about the primordial Universe, called “Cosmic Inflation,” predicts:

•

The expansion of our Universe accelerated in a tiny fraction of a second after its birth.

•

Just like Dark Energy accelerating today’s expansion: the acceleration also happened at very, very early times!

•

Inflation stretches “micro to macro”

•

In a tiny fraction of a second, the size of an atomic nucleus (~10^-15m) would be stretched to 1 A.U. (~10¹¹m), at least.

53

(Starobinsky 1980; Sato 1981; Guth 1981;

Linde 1982; Albrecht & Steinhardt 1982; Starobinsky 1980)

(54)

Cosmic Inflation = Very Early Dark Energy

54

(55)

Origin of Fluctuations

•

OK, back to the cosmic hot soup.

•

The sound waves were created when we perturbed it.

•

^{“We”? Who?}

•

Who actually perturbed the cosmic soup?

•

Who generated the original (seed) ripples?

55

(56)

WMAP 9-year Power Spectrum

about

1 degree on the sky COBE

56

(57)

Getting rid of the Sound Waves

57

Primordial Ripples

(58)

The Early Universe Could Have Done This Instead

58

More Power on Large Scales

Small Scale Large Scale

(59)

...or, This.

59

More Power on Small Scales

(60)

...or, This.

60

Parametrization:

l(l+1)C l ~ l ^ns–1

And, inflation predicts n s ~1

(61)

Theory Says...

•

The leading theoretical idea about the primordial Universe, called “Cosmic Inflation,” predicts:

•

The expansion of our Universe accelerated in a tiny fraction of a second after its birth.

•

the primordial ripples were created by quantum fluctuations during inflation, and

•

how the power is distributed over the scales is

determined by the expansion history during cosmic inflation.

•

Measurement of ns gives us this remarkable information!

61

(62)

Quantum Fluctuations

•

You may borrow a lot of energy from vacuum if you promise to return it to the vacuum immediately.

•

The amount of energy you can borrow is inversely proportional to the time for which you borrow the energy from the vacuum.

62

Heisenberg’s Uncertainty Principle

(63)

(Scalar) Quantum Fluctuations

•

Why is this relevant?

•

The cosmic inflation (probably) happened when the Universe was a tiny fraction of second old.

•

Something like 10^-36 second old

•

(Expansion Rate) ~ 1/(Time)

•

which is a big number! (~10¹²GeV)

•

Quantum fluctuations were important during inflation!

δφ = (Expansion Rate)/(2π) [in natural units]

63

Mukhanov & Chibisov (1981); Guth & Pi (1982); Starobinsky (1982); Hawking (1982);

Bardeen, Turner & Steinhardt (1983)

(64)

Stretching Micro to Macro

Macroscopic size at which gravity becomes important

Quantum fluctuations on microscopic scalesδφ INFLATION!

Quantum fluctuations cease to be quantum, and become observable!δφ ⁶⁴

(65)

Inflation Offers a Magnifier for Microscopic World

•

Using the power spectrum of primordial fluctuations imprinted in CMB, we can observe the quantum phenomena at the

ultra high-energy scales that would never be reached by the particle accelerator.

• Measured value (WMAP 9-year data only):

n

s

= 0.972 ± 0.013 (68%CL)

₆₅

(66)

66

1000

100

South Pole Telescope [10-m in South Pole]

Atacama Cosmology Telescope [6-m in Chile]

(67)

67

1000

100

South Pole Telescope [10-m in South Pole]

Atacama Cosmology Telescope [6-m in Chile]

n

s

= 0.965 ± 0.010 (68%CL)

(68)

•

Quantum fluctuations also generate ripples in space- time, i.e., gravitational waves, by the same mechanism.

•

Primordial gravitational waves generate temperature

anisotropy in CMB, as well as polarization in CMB with a distinct pattern called “B-mode polarization.”

h = (Expansion Rate)/(2^1/2πM_planck) [in natural units]

[h = “strain”]

68

(Tensor) Quantum Fluctuations, a.k.a. Gravitational Waves

Starobinsky (1979)

(69)

WMAP9

+ACT+SPT WMAP9

+ACT+SPT +BAO+H0

69

(70)

The Question

•

Has inflation actually occurred?

•

We do not know for sure, but we have some compelling evidence in our hand.

•

What does it take to prove inflation?

•

Determination of the B-mode power spectrum

•

Can we falsify inflation?

•

Yes (sort of).

(71)

Falsifying single-field inflation using the Bispectrum

•

Three-point function!

•

^B^ζ^(k¹^,k²^,k³⁾

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

71

model-dependent function

k1

k2

k3

Primordial fluctuation ”fNL”

(72)

MOST IMPORTANT

(73)

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 95% CL limits are:

•

^f^NL^{= 37}± 20 (68%CL)

•

The WMAP data are consistent with the prediction of

simple single-field inflation models: 1–ns≈r≈fNL ₇₃

(74)

Summary

•

WMAP has completed 9 years of observations.

•

We could determine the age, composition, expansion rate, etc., from CMB.

•

We could even push the boundary farther back in time, probing the origin of fluctuations in the very early

Universe: inflationary epoch at ultra-high energies.

•

Next Big Thing: Primordial gravitational waves.

•

The 3-point function: Powerful test of inflation.

74

(75)

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

⁷⁵

(76)

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) 76

ln(τ_NL)

77 3.3x10⁴

(Smidt et al. 2010)

(77)

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

77

(78)

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 78

(79)

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

79