Although we cannot be there physically, we can observe the phenomena in the early Universe using powerful telescopes

Cosmic Microwave Background

Eiichiro Komatsu (Max-Planck-Institut für Astrophysik) IMPRS Advanced Course, February 3, 2017

Seeing the Early Universe

•

Astronomers often talk about the early Universe as if they were there to see it…

•

The stories told by astronomers are remarkable, but aren’t they just imaginations of astronomers?

•

Although we cannot be there physically, we can observe the phenomena in the early Universe using powerful telescopes

•

We are not making stuff up!

•

The goal of my lectures is to show you

how we are seeing and studying the early Universe directly using the light from the epoch of the fireball Universe

Seeing the Early Universe

From “Cosmic Voyage”

Fireball Universe

Hot and Dense

Time

Space

Hot and Dense

Hot

Expansion

Fireball Universe

Time

Space

Hot Cooled down

Hot and Dense

Expansion Expansion Fireball Universe

Time

Space

Definitive Result

•

Those photons which filled the fireball Universe are still with us

•

There are 411 such photons per cubic centimetre

•

Due to the expansion of space and cooling down, these photons are cold, and their

wavelength is in the radio/microwave region

All you need to do is to detect radio

waves. For example, 1% of noise on the TV is from the fireball Universe

Dr. Hiranya Peiris

（University College London）

Night Sky in Optical (~0.5µm)

10

Night Sky in Microwave (~1mm)

11

Night Sky in Microwave (~1mm)

12

Light from the fireball Universe filling our sky

The Cosmic Microwave Background (CMB)

１９６５

Arno Penzias & Robert Wilson, 1965

14

• ^Isotropic

1:25 model at Deutsches Museum

15

The REAL back-end system of the Penzias-Wilson experiment, exhibited at Deutsches Museum

Donated by Dr. Penzias, who was born in Munich

Arno Penzias

16

17

18

May 20, 1964

CMB“Discovere d”

19

6.7–2.3–0.8–0.1

= 3.5±1.0 K

Proof of the

fireball universe

4K Black-body

2.725K Black-body 2K Black-body

Rocket (COBRA)

Satellite (COBE/FIRAS) CN Rotational Transition Ground-based

Balloon-borne

Satellite (COBE/DMR)

Wavelength

30cm 3m

Bri gh tn ess, W /m

/sr/ H z

20

(from Samtleben et al. 2007)

Fireball Universe, Observed

•

The Planck spectrum is achieved only when matter and radiation are exchanging energies frequently

•

Called “thermal equilibrium”

•

Today’s Universe is not in thermal equilibrium (we die otherwise), which means that the

Universe was in thermal equilibrium in the

past - fireball Universe [Urknalls]

How was CMB created?

• When the Universe was hot...

• The Universe was a hot soup made of:

• Protons, electrons, and helium nuclei

• Photons and neutrinos

• Dark matter

22

Universe as a hot soup

• Free electrons can scatter photons

efficiently.

• Photons cannot go very far.

proton helium

electron

photon

23

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.

Ti me

1500K

6000K

3000K

proton helium electron photon

H + photon –> p + e

Ionization

Recombination

p + e

–> H + photon

X=0.5; the universe is half ionized, and half

recombined at T~3700 K

25

photons are

frequently scattered

decoupling at T~3000 K

26

COBE/DMR, 1992

•Isotropic?

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

level)

Smoot et al. (1992)

1cm

6mm

3mm

A spare unit of COBE/DMR ( λ =1cm)

Donated by Prof. George Smoot, the PI of DMR

George Smoot

COBE to WMAP (x35 better resolution)

COBE

WMAP

COBE 1989

WMAP

2001 ³⁰

WMAP at Lagrange 2 (L2) Point

• L2 is 1.5 million kilometers from Earth

• WMAP leaves Earth, Moon, and Sun

behind it to avoid radiation from them

Wilkinson Microwave Anisotropy Probe

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

32

23 GHz [unpolarized]

33

33 GHz [unpolarized]

34

41 GHz [unpolarized]

35

61 GHz [unpolarized]

36

94 GHz [unpolarized]

37

Planck 2013 Release

How many components?

1. ^{CMB: T}

^{~ ν}

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

~ ν

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

~ ν

4. Dust (heated dust emitting thermal emission): T

~ν

5. Spinning dust (rapidly rotating tiny dust grains):

T

~complicated

You need at least five frequencies to separate them!

A direct image of the Universe when it was 3000 K.

40

How were these ripples created?

41

Have you dropped potatoes in a soup?

• What would happen if you “perturb” the soup?

42

The Cosmic Sound Wave

43

Can You See the Sound Wave?

44

Analysis:

2-point Correlation

•C(θ)=(1/4π)∑(2l+1)C

P

(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

45

θ

COBE

WMAP

COBE/DMR Power Spectrum Angle ~ 180 deg / l

Angular Wavenumber, l

~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?

47

θ

COBE

WMAP

θ

WMAP Power Spectrum

Ang ul ar Po w er Spectrum Large Scale Small Scale about

1 degree on the sky COBE

48

The Cosmic Sound Wave

• “The Universe as a 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.

CMB to Baryon & Dark Matter

Baryon Density (Ω

)

Total Matter Density (Ω

)

=Baryon+Dark Matter

51

By “baryon,” I mean hydrogen and helium.

Long Wavelength Short Wavelength

Measuring Abundance of H&He

Amplitude of W aves [ μ K

]

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

]

180 degrees/(angle in the sky)

Long Wavelength Short Wavelength

Measuring Total Matter Density

Cosmic Pie Chart

• Cosmological observations (CMB, galaxies, supernovae) over the last decade told us

that we don’t understand much of the Universe.

Hydrogen & Helium Dark Matter

Dark Energy ⁵⁴

Matter and Expansion

• How would an empty universe expand?

–Answer： Constant-velocity expansion (no acceleration or deceleration)

• How would a universe with matter expand?

–Answer：Gravity from matter slows down the expansion (deceleration)

• A universe with too much matter will collapse again

–Going back to a fireball universe!

Hot Universe Hot Universe

“Big Bang” “Big Crunch”

55

Accelerating Universe

• How would a universe with matter expand?

–Answer：Gravity from matter slows down the expansion (deceleration)

• This contradicts with observations!

– Matter cannot do it

– Some kind of invisible non-material energy:

• Dark Energy

Hot Universe

“Big Bang”

56

Imagine throwing an apple

57

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?

60

Leading Idea

• Quantum Mechanics at work in the early Universe

• Uncertainty Principle:

• [Energy you can borrow] x [Time you borrow] ~ h

• Time was very short in the early Universe = You could borrow a lot of energy

• Those energies became the origin of fluctuations

• How did quantum fluctuations on the microscopic scales become macroscopic fluctuations over cosmological

sizes?

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

Bardeen, Turner & Steinhardt (1983)

Cosmic Inflation

• In a tiny fraction of a second, the size of an atomic nucleus became the size of the Solar System

• In 10^–36 second, space was stretched by at least a factor of 10²⁶

Starobinsky (1980); Sato (1981); Guth (1981); Linde (1982); Albrecht & Steinhardt (1982)

Stretching Micro to Macro

Inflation!

Quantum fluctuations on microscopic scales

• Quantum fluctuations cease to be quantum

• Become macroscopic, classical fluctuations

Key Predictions of Inflation

• Fluctuations we observe today in CMB and the matter distribution originate from quantum

fluctuations generated during inflation

• There should also be ultra-long-wavelength

gravitational waves generated during inflation

ζ

scalar mode

h ij

tensor mode

We measure distortions in space

• A distance between two points in space

• ζ: “curvature perturbation” (scalar mode)

• Perturbation to the determinant of the spatial metric

• hij: “gravitational waves” (tensor mode)

• Perturbation that does not change the determinant (area)

d`

= a

(t)[1 + 2⇣ (x, t)][

+ h

(x, t)]dx

dx

X

i

h_ii = 0

Heisenberg’s

Uncertainty Principle

• [Energy you can borrow] x [Time you borrow] = constant

• Suppose that the distance between two points

increases in proportion to a(t) [which is called the scale factor] by the expansion of the universe

• Define the “expansion rate of the universe” as H ⌘ a˙

a [This has units of 1/time]

Fluctuations are proportional to H

• [Energy you can borrow] x [Time you borrow] = constant

•

• Then, both ζ and hij are proportional to H

• Inflation occurs in 10^–36 second - this is such a short period of time that you can borrow a lot of energy! H during inflation in energy units is 10¹⁴ GeV

H ⌘ a˙

a [This has units of 1/time]

Long Wavelength Short Wavelength

180 degrees/(angle in the sky) Amplitude of W aves [ μ K

]

WMAP Collaboration

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

]

Removing Ripples:

Power Spectrum of

Primordial Fluctuations

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

]

Removing Ripples:

Power Spectrum of

Primordial Fluctuations

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

]

Removing Ripples:

Power Spectrum of

Primordial Fluctuations

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

]

Let’s parameterise like

Wave Amp. / ` ^{n s 1}

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

]

Wave Amp. / ` ^{n s 1}

WMAP 9-Year Only:

n

=0.972±0.013 (68%CL)

2001–2010

South Pole Telescope [10-m in South Pole]

Atacama Cosmology Telescope [6-m in Chile]

Amplitude of W aves [ μ K

]

1000

100

2001–2010

1000

100

South Pole Telescope [10-m in South Pole]

Atacama Cosmology Telescope [6-m in Chile]

Amplitude of W aves [ μ K

]

n

=0.965±0.010

2001–2010

1000

100

South Pole Telescope [10-m in South Pole]

Atacama Cosmology Telescope [6-m in Chile]

Amplitude of W aves [ μ K

]

2001–2010

n

=0.961±0.008

~5σ discovery of ns<1 from the CMB data combined

with SDSS

Res id ua l

Planck 2013 Result!

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

]

2009–2013

Res id ua l

Planck 2013 Result!

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

]

2009–2013

n

=0.960±0.007

First >5σ discovery of ns<1 from the CMB data alone

Predicted in 1981.

Finally discovered in 2013 by WMAP and Planck

•Inflation must end

•Inflation predicts n_s~1, but not exactly equal to 1. Usually n_s<1 is expected

•The discovery of n_s<1 has been the dream of cosmologists since 1992, when the CMB anisotropy was first

discovered and n_s~1 (to within 30%)

was indicated Slava Mukhanov said in

his 1981 paper that ns should be less than 1

How do we know that

primordial fluctuations were of

quantum mechanical origin?

[Values of Temperatures in the Sky Minus 2.725 K] / [Root Mean Square]

Fraction of the Number of Pixels Having Those T emperatur es

Quantum Fluctuations give a Gaussian distribution of

temperatures.

Do we see this

in the WMAP data?

[Values of Temperatures in the Sky Minus 2.725 K] / [Root Mean Square]

Fraction of the Number of Pixels Having Those T emperatur es

YES!!

Histogram: WMAP Data

Red Line: Gaussian

Testing Gaussianity

[Values of Temperatures in the Sky Minus 2.725 K]/ [Root Mean Square]

Fraction of the Number of Pixels Having Those Temperatures

Histogram: WMAP Data Red Line: Gaussian

Since a Gauss distribution is symmetric, it must yield a vanishing 3-point function

More specifically, we measure this using temperatures at

three different locations and average:

h T ³i ⌘

Z ₁

1

d T P ( T ) T ³

h T (ˆ n

) T (ˆ n

) T (ˆ n

) i

Non-Gaussianity:

A Powerful Test of Quantum Fluctuations

•

The WMAP data show that the distribution of

temperature fluctuations of CMB is very precisely Gaussian

•

with an upper bound on a deviation of 0.2%

•

With improved data provided by the Planck

mission, the upper bound is now 0.03%

CMB Research:

Next Frontier

Primordial

Gravitational Waves

Extraordinary claims require extraordinary evidence.

The same quantum fluctuations could also generate gravitational waves, and we wish to find them

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

• Primordial gravitational waves generate temperature anisotropy in CMB.

h = (Expansion Rate)/(2

πM

) [in natural units]

[h = “strain”]

86

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

Starobinsky (1979)

Gravitational waves are coming toward you!

• What do they do to the distance between particles? ⁸⁷

Two GW modes

88

Measuring GW

• GW changes the distances between two points

d`² = dx² = X

ij

ij dxⁱdx^j

d`² = X

ij

( _ij + h_ij )dxⁱdx^j

Laser Interferometer

Mirror

Mirror

detector _{No signal}

Laser Interferometer

Mirror

Mirror

Signal!

detector

Laser Interferometer

Mirror

Mirror

Signal!

detector

LIGO detected GW from binary blackholes, with the wavelength

of thousands of kilometres

But, the primordial GW affecting the CMB has a wavelength of

billions of light-years!! How

do we find it?

Detecting GW by CMB

Isotropic electro-magnetic fields

Detecting GW by CMB

GW propagating in isotropic electro-magnetic fields

hot

hot

cold

cold

cold cold

hot hot

Detecting GW by CMB

Space is stretched => Wavelength of light is also stretched

hot

hot

cold

cold

cold cold

hot hot

Detecting GW by CMB Polarisation

electron electron

Space is stretched => Wavelength of light is also stretched

GW to temperature anisotropy

hot

hot

cold

cold

cold cold

hot hot

• Stretching of space -> temperature drops

• Contraction of space -> temperature rises

98

We measure distortions in space

• A distance between two points in space

• ζ: “curvature perturbation” (scalar mode)

• Perturbation to the determinant of the spatial metric

• hij: “gravitational waves” (tensor mode)

• Perturbation that does not change the determinant (area)

d`

= a

(t)[1 + 2⇣ (x, t)][

+ h

(x, t)]dx

dx

X

i

h_ii = 0

99

Tensor-to-scalar Ratio

• The BICEP2 results suggest r~0.2, if we do not subtract any foregrounds

r ⌘ h h _ij h ^ij i h ⇣ ² i

100

Limit from Temperature

r=0.2 r=1.2

WMAP5

101

WMAP9

+ACT+SPT WMAP9

+ACT+SPT +BAO+H

102

WMAP 9-year results

(Hinshaw, Larson, Komatsu, et al. 2012)

Planck confirms our results

103

Planck Collaboration XXII (2013)

r<0.12 (95%CL)

CMB Polarisation

• CMB is [weakly] polarised!

104

Light waves oscillate in various directions. We say “light is polarised,” when one particular direction dominates

Polarisation of Light

Sun light reflected by the surface of the sea is polarised horizontally. Using sunglasses transmitting only vertical polarisation eliminates the reflected sun

light

Ex. 1: Reflection by Sea

horizontally polarised

Ex. 2: Windshield

Scattering by electrons makes CMB polarised in various directions

Ex. 3: CMB

Stokes Parameters

North

East ¹¹⁰

Stokes Q Stokes U

23 GHz

WMAP Collaboration

111

Stokes Q Stokes U North

East

WMAP Collaboration

23 GHz [13 mm]

112

Stokes Q Stokes U

WMAP Collaboration

33 GHz [9.1 mm]

113

Stokes Q Stokes U

WMAP Collaboration

41 GHz [7.3 mm]

114

Stokes Q Stokes U

WMAP Collaboration

61 GHz [4.9 mm]

115

Stokes Q Stokes U

WMAP Collaboration

94 GHz [3.2 mm]

116

How many components?

• CMB: Tν ~ ν⁰

• Synchrotron: Tν ~ ν^–3

• Dust: Tν ~ ν²

• Therefore, we need at least 3 frequencies to separate them

117

Physics of CMB Polarisation

• Necessary and sufficient conditions for generating polarisation in CMB:

• Thomson scattering

• Quadrupolar temperature anisotropy around an electron

By Wayne Hu

118

Origin of Quadrupole

• Scalar perturbations: motion of electrons with respect to photons

• Tensor perturbations: gravitational waves

119

Seeing polarisation in the WMAP data

• Average polarisation data around cold and hot temperature spots

• Outside of the Galaxy

mask [not shown], there are 11536 hot spots and 11752 cold spots

• Averaging them beats

the noise down ¹²⁰

Radial and tangential polarisation around

temperature spots

• This shows polarisation

generated by the plasma flowing into gravitational potentials

• Signatures of the “scalar mode” fluctuations in

polarisation

• These patterns are called

“E modes”

WMAP Collaboration

121

Planck Data!

Planck Collaboration

122

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

Two GW modes

• Anisotropic stretching of space generates quadrupole temperature anisotropy. How?

124

GW to temperature anisotropy

electrons

125

GW to temperature anisotropy

hot

hot

cold

cold

cold cold

hot hot

• Stretching of space -> temperature drops

• Contraction of space -> temperature rises

126

Then to polarisation!

hot

hot

cold

cold

cold cold

hot hot

• Polarisation directions are parallel to hot regions

127

• No detection of B-mode polarization at degree scales, before March 17

Po la ri za tio n Po w er Spectrum

128

March 17, 2014

BICEP2’s announcement

130

*Courtesy of Yuji Chinone, with the POLARBEAR data points

March 17, 2014: CMB Polarisation by gravitational waves discovered?

What is BICEP2?

• A small [26 cm] refractive telescope at South Pole

• 512 bolometers working at 150 GHz

• Observed 380 square degrees for three years [2010-2012]

• Previous: BICEP1 at 100 and 150 GHz [2006-2008]

• On-going: Keck Array = 5 x BICEP2 at 150 GHz

[2011-2013] and additional detectors at 100 and 220

GHz [2014-] ¹³³

Let’s try to understand what is shown in this plot, assuming that it is due to gravitational waves

Signature of gravitational waves in the sky [?]

BICEP2 Collaboration

134

propagation direction of GW h+=cos(kx)

Polarisation directions perpendicular/parallel to the wavenumber vector -> E

mode polarisation ¹³⁵

propagation direction of GW hx=cos(kx)

Polarisation directions 45 degrees tilted from to the wavenumber vector -> B

mode polarisation ¹³⁶

Important note:

• Definition of h+ and hx depends on coordinates, but definition of E- and B-mode polarisation does not

depend on coordinates

• Therefore, h+ does not always give E; hx does not always give B

• The important point is that h+ and hx always

coexist. When a linear combination of h+ and hx

produces E, another combination produces B

137

CAUTION: we are NOT seeing a single plane wave propagating perpendicular to our line of sight

Signature of gravitational waves in the sky [?]

BICEP2 Collaboration

138

CAUTION: we are NOT seeing a single plane wave propagating perpendicular to our line of sight

Signature of gravitational waves in the sky [?]

if you wish, you could associate one pattern with one plane wave…

BUT

139

The E-mode polarisation is totally dominated by the scalar-mode fluctuations [density waves]

There are E modes in the sky as well

BICEP2 Collaboration BICEP2 Collaboration

140

Is the signal cosmological?

•

Worries:

•

Is it from Galactic foreground emission, e.g., dust?

•

Is it from imperfections in the experiment, e.g., detector mismatches?

141

142

143

Analysis: Two-point Correlation Function

θ

C(✓) = 1 4⇡

X

`

(2` + 1)C<sub>`</sub>P_{`</sub>(cos ✓) C<sub>`} is the “power spectrum” with

` ⇡ ⇡

✓

144

x: 150GHz x 100GHz [BICEP1]

*: 150GHz x 150GHz [BICEP1]

No 100 GHz x 100 GHz [yet]

BICEP2 Collaboration

145

Can we rule out synchrotron or dust?

• The answer is No

BICEP2 Collaboration

146

September 22, 2014

Planck’s Intermediate Paper on Dust

147

• Values of the “tensor-to-scalar ratio” equivalent to the B-mode power spectrum seen at various locations in the sky

Area observed by BICEP2

Planck Collaboration

148

• Planck measured the B-mode power spectrum at 353 GHz well

• Extrapolating it down to 150 GHz appears to explain all of the signal seen by BICEP2…

Planck Collaboration

149

•

Planck shows the evidence that the detected signal is not cosmological, but is due to dust

•

No strong evidence that the detected signal is cosmological

The search continues!!

Current Situation

1989–1993 2001–2010 2009–2013 202X–

ESA

2025– [proposed]

JAXA

+ possibly NASA

LiteBIRD

2025– [proposed]

Target uncertainty: δr=0.001 100 times better than

the current upper bound on the

gravitational wave amplitude