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(1)

Finding

Cosmic Inflation

Eiichiro Komatsu [MPI für Astrophysik]

Colloquium, MPI für Radioastronomie

24. Mai, 2019

(2)
(3)

Full-dome movie for planetarium Director: Hiromitsu Kohsaka

(4)
(5)
(6)

B-mode from gravitational lensing E-mode

from sound waves

Temperature from sound waves

B-mode from GW

Seven or ders of magnitude in power in “just” 25 years

(7)

B-mode from gravitational lensing E-mode

from sound waves

Temperature from sound waves

B-mode from GW

Seven or ders of magnitude in power in “just” 25 years

We want this!!

(8)

E-mode

from sound waves

Temperature from sound waves

B-mode from GW

Another two or ders of magnitude in the next 10–15 years

B-mode from gravitational lensing

We want this!!

(9)

ESA

2025– [proposed]

JAXA

LiteBIRD

2027– [proposed]

+ participations from USA, Canada, Europe

Polarisation satellite dedicated to measure CMB polarisation from

primordial GW, with a few thousand

TES bolometers in space

(10)

ESA

2025– [proposed]

JAXA

LiteBIRD

2027– Selected!

May 21: JAXA has chosen LiteBIRD as the strategic large-class mission.

We will go to L2!

+ participations from

USA, Canada, Europe

(11)

A Remarkable Story

• Observations of the cosmic microwave background and their interpretation

taught us that galaxies, stars, planets, and ourselves originated from tiny

fluctuations in the early Universe

But, what generated the initial

fluctuations?

(12)

Leading Idea

Quantum mechanics at work in the early Universe

“We all came from quantum fluctuations”

But, how did quantum fluctuations on the microscopic scales become macroscopic fluctuations over large

distances?

What is the missing link between small and large scales?

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

Bardeen, Turner & Steinhardt (1983)

(13)

Cosmic Inflation

Exponential expansion (inflation) stretches the wavelength of quantum fluctuations to cosmological scales

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

Quantum fluctuations on microscopic scales

Inflation!

(14)

Key Predictions

Fluctuations we observe today in CMB and the matter distribution originate from quantum fluctuations during inflation

ζ

scalar mode

h ij

tensor mode

There should also be ultra long-wavelength gravitational waves generated during inflation

Grishchuk (1974) Starobinsky (1979) Mukhanov&Chibisov (1981) Guth & Pi (1982)

Hawking (1982)

Starobinsky (1982)

Bardeen, Steinhardt&Turner (1983)

(15)

We measure distortions in space

A distance between two points in space

d`

2

= a

2

(t)[1 + 2⇣ (x, t)][

ij

+ h

ij

(x, t)]dx

i

dx

j

X

i

h

ii

= 0

ζ : “curvature perturbation” (scalar mode)

Perturbation to the determinant of the spatial metric

hij : “gravitational waves” (tensor mode)

Perturbation that does not alter the determinant

(16)

We measure distortions in space

A distance between two points in space

d`

2

= a

2

(t)[1 + 2⇣ (x, t)][

ij

+ h

ij

(x, t)]dx

i

dx

j

X

i

h

ii

= 0

ζ : “curvature perturbation” (scalar mode)

Perturbation to the determinant of the spatial metric

hij : “gravitational waves” (tensor mode)

Perturbation that does not alter the determinant

scale factor

(17)

Finding Inflation

Inflation is the accelerated, quasi-exponential expansion.

Defining the Hubble expansion rate as H(t)=dln(a)/dt, we must find

¨ a

a = ˙ H + H

2

> 0 ✏ ⌘ H ˙

H

2

< 1

For inflation to explain flatness of spatial geometry of our observable Universe, we need to have a sustained period of inflation. This implies ε=O(N–1) or smaller, where N is

the number of e-folds of expansion counted from the end of inflation:

N ⌘ ln a end

a =

Z t

end

t

dt 0 H (t 0 ) ⇡ 50

(18)

Have we found inflation?

Have we found ε << 1?

To achieve this, we need to map out H(t), and show that it does not change very much with time

We need the “Hubble diagram” during inflation!

✏ ⌘ H ˙

H

2

< 1

(19)

Fluctuations are proportional to H

Both scalar (ζ) and tensor (hij) perturbations are proportional to H

Consequence of the uncertainty principle

[energy you can borrow] ~ [time you borrow]–1 ~ H

THE KEY: The earlier the fluctuations are generated, the more its wavelength is stretched, and thus the bigger the angles they subtend in the sky. We can map H(t) by

measuring CMB fluctuations over a wide range of angles

(20)

Fluctuations are proportional to H

We can map H(t) by measuring CMB fluctuations over a wide range of angles

1. We want to show that the amplitude of CMB fluctuations does not depend very much on angles

2. Moreover, since inflation must end, H would be a

decreasing function of time. It would be fantastic to show that the amplitude of CMB fluctuations actually DOES depend on angles such that the small scale has slightly smaller power

(21)

• Decompose temperature

fluctuations in the sky into a set of waves with various

wavelengths

• Make a diagram showing the strength of each wavelength

Data Analysis

(22)

Long Wavelength Short Wavelength

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

2

]

WMAP Collaboration

(23)
(24)

Kosmische Miso Suppe

When matter and radiation were hotter than 3000 K, matter was completely ionised. The Universe was

filled with plasma, which behaves just like a soup

Think about a Miso soup (if you know what it is).

Imagine throwing Tofus into a Miso soup, while changing the density of Miso

And imagine watching how ripples are created and

propagate throughout the soup

(25)
(26)

Long Wavelength Short Wavelength

Measuring Abundance of H&He

Amplitude of W aves [ μ K 2 ]

180 degrees/(angle in the sky)

(27)

Amplitude of W aves [ μ K 2 ]

180 degrees/(angle in the sky)

Long Wavelength Short Wavelength

Measuring Total Matter Density

(28)

Origin of Fluctuations

Who dropped those Tofus into the cosmic Miso

soup?

(29)

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

2

]

Long Wavelength Short Wavelength

Removing Ripples:

Power Spectrum of

Primordial Fluctuations

(30)

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

2

]

Long Wavelength Short Wavelength

Removing Ripples:

Power Spectrum of

Primordial Fluctuations

(31)

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

2

]

Long Wavelength Short Wavelength

Removing Ripples:

Power Spectrum of

Primordial Fluctuations

(32)

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

2

]

Long Wavelength Short Wavelength

Let’s parameterise like

Wave Amp. / ` n s 1

(33)

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

2

]

Long Wavelength Short Wavelength

Wave Amp. / ` n s 1

COBE 2-Year Limit!

n s =1.25 +0.4–0.45 (68%CL)

1989–1993

l=3–30

Wright, Smoot, Bennett & Lubin (1994)

In 1994:

(34)

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

2

]

Long Wavelength Short Wavelength

Wave Amp. / ` n s 1

WMAP 9-Year Only:

n s =0.972±0.013 (68%CL)

2001–2010

WMAP Collaboration

20 years later…

(35)

1000

100

South Pole Telescope [10-m in South Pole]

Atacama Cosmology Telescope [6-m in Chile]

Amplitude of W aves [ μ K

2

]

n s =0.965±0.010

2001–2010

WMAP Collaboration

(36)

1000

100

South Pole Telescope [10-m in South Pole]

Atacama Cosmology Telescope [6-m in Chile]

Amplitude of W aves [ μ K

2

]

2001–2010

n s =0.961±0.008

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

distribution of galaxies

WMAP Collaboration

(37)

Res id ua l

Planck 2013 Result!

180 degrees/(angle in the sky)

Amplitude of W aves [ μ K

2

]

2009–2013

n s =0.960±0.007

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

[Planck+WMAP]

(38)

[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?

(39)

[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

WMAP Collaboration

(40)

Testing Gaussianity

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

[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

h T

3

i ⌘

Z

1

1

d T P ( T ) T

3

More specifically, we measure this by averaging the product of temperatures at three

different locations in the sky

h T (ˆ n

1

) T (ˆ n

2

) T (ˆ n

3

) i

(41)

Lack of non-Gaussianity

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% (95%CL)

⇣ (x) = ⇣

gaus

(x) + 3

5 f

NL

gaus2

(x)

with

f

NL

= 37 ± 20 (68% CL)

The Planck data improved the upper bound by an order of magnitude: deviation is <0.03% (95%CL)

f

NL

= 0.8 ± 5.0 (68% CL)

WMAP 9-year Result

Planck 2015 Result

(42)

So, have we found inflation?

Single-field slow-roll inflation looks remarkably good:

Super-horizon fluctuation

Adiabaticity

Gaussianity

ns<1

What more do we want? Gravitational waves. Why?

Because the “extraordinary claim requires extraordinary evidence”

(43)

Gravitational waves as the quantum vacuum fluctuation in spacetime

Quantising the gravitational waves in de Sitter space in vacuum

Grishchuk (1974); Starobinsky (1979)

⇤ h ij = 0

<latexit sha1_base64="uViT66houmc5QHCDnmBMnjkyDno=">AAAB+HicbVBNSwMxEJ31s9aPrnr0EiyCp7Irgl6EUi8eK9gPaJclm6ZtbDZZkqxYl/4SLx4U8epP8ea/MW33oK0PBh7vzTAzL0o408bzvp2V1bX1jc3CVnF7Z3ev5O4fNLVMFaENIrlU7QhrypmgDcMMp+1EURxHnLai0fXUbz1QpZkUd2ac0CDGA8H6jGBjpdAtdWvyEQ3DjN1P0BXyQrfsVbwZ0DLxc1KGHPXQ/er2JEljKgzhWOuO7yUmyLAyjHA6KXZTTRNMRnhAO5YKHFMdZLPDJ+jEKj3Ul8qWMGim/p7IcKz1OI5sZ4zNUC96U/E/r5Oa/mWQMZGkhgoyX9RPOTISTVNAPaYoMXxsCSaK2VsRGWKFibFZFW0I/uLLy6R5VvG9in97Xq7W8jgKcATHcAo+XEAVbqAODSCQwjO8wpvz5Lw4787HvHXFyWcO4Q+czx8805Il</latexit><latexit sha1_base64="uViT66houmc5QHCDnmBMnjkyDno=">AAAB+HicbVBNSwMxEJ31s9aPrnr0EiyCp7Irgl6EUi8eK9gPaJclm6ZtbDZZkqxYl/4SLx4U8epP8ea/MW33oK0PBh7vzTAzL0o408bzvp2V1bX1jc3CVnF7Z3ev5O4fNLVMFaENIrlU7QhrypmgDcMMp+1EURxHnLai0fXUbz1QpZkUd2ac0CDGA8H6jGBjpdAtdWvyEQ3DjN1P0BXyQrfsVbwZ0DLxc1KGHPXQ/er2JEljKgzhWOuO7yUmyLAyjHA6KXZTTRNMRnhAO5YKHFMdZLPDJ+jEKj3Ul8qWMGim/p7IcKz1OI5sZ4zNUC96U/E/r5Oa/mWQMZGkhgoyX9RPOTISTVNAPaYoMXxsCSaK2VsRGWKFibFZFW0I/uLLy6R5VvG9in97Xq7W8jgKcATHcAo+XEAVbqAODSCQwjO8wpvz5Lw4787HvHXFyWcO4Q+czx8805Il</latexit><latexit sha1_base64="uViT66houmc5QHCDnmBMnjkyDno=">AAAB+HicbVBNSwMxEJ31s9aPrnr0EiyCp7Irgl6EUi8eK9gPaJclm6ZtbDZZkqxYl/4SLx4U8epP8ea/MW33oK0PBh7vzTAzL0o408bzvp2V1bX1jc3CVnF7Z3ev5O4fNLVMFaENIrlU7QhrypmgDcMMp+1EURxHnLai0fXUbz1QpZkUd2ac0CDGA8H6jGBjpdAtdWvyEQ3DjN1P0BXyQrfsVbwZ0DLxc1KGHPXQ/er2JEljKgzhWOuO7yUmyLAyjHA6KXZTTRNMRnhAO5YKHFMdZLPDJ+jEKj3Ul8qWMGim/p7IcKz1OI5sZ4zNUC96U/E/r5Oa/mWQMZGkhgoyX9RPOTISTVNAPaYoMXxsCSaK2VsRGWKFibFZFW0I/uLLy6R5VvG9in97Xq7W8jgKcATHcAo+XEAVbqAODSCQwjO8wpvz5Lw4787HvHXFyWcO4Q+czx8805Il</latexit><latexit sha1_base64="uViT66houmc5QHCDnmBMnjkyDno=">AAAB+HicbVBNSwMxEJ31s9aPrnr0EiyCp7Irgl6EUi8eK9gPaJclm6ZtbDZZkqxYl/4SLx4U8epP8ea/MW33oK0PBh7vzTAzL0o408bzvp2V1bX1jc3CVnF7Z3ev5O4fNLVMFaENIrlU7QhrypmgDcMMp+1EURxHnLai0fXUbz1QpZkUd2ac0CDGA8H6jGBjpdAtdWvyEQ3DjN1P0BXyQrfsVbwZ0DLxc1KGHPXQ/er2JEljKgzhWOuO7yUmyLAyjHA6KXZTTRNMRnhAO5YKHFMdZLPDJ+jEKj3Ul8qWMGim/p7IcKz1OI5sZ4zNUC96U/E/r5Oa/mWQMZGkhgoyX9RPOTISTVNAPaYoMXxsCSaK2VsRGWKFibFZFW0I/uLLy6R5VvG9in97Xq7W8jgKcATHcAo+XEAVbqAODSCQwjO8wpvz5Lw4787HvHXFyWcO4Q+czx8805Il</latexit>

gives

k 3 h h ij (k)h ij (k 0 ) i

= (2⇡ ) 3 D (k k 0 ) 8 M pl 2

✓ H 2⇡

2

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scale-invariant spectrum

(44)

Theoretical energy density

Watanabe & EK (2006)

GW entered the horizon during the radiation era

GW entered the horizon during the matter era

Spectrum of GW today

(45)

Spectrum of GW today

Watanabe & EK (2006)

CMB PTA Interferometers

Wavelength of GW

~ Billions of light years!!!

Theoretical energy density

(46)

Measuring GW

d`

2

= dx

2

= X

ij

ij

dx

i

dx

j

d`

2

= X

ij

(

ij

+ h

ij

)dx

i

dx

j

GW changes distances between two points

(47)

Laser Interferometer

Mirror

Mirror

detector No signal

(48)

Laser Interferometer

Mirror

Mirror

Signal!

detector

(49)

LIGO detected GW from a 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?

(50)

Detecting GW by CMB

Isotropic electro-magnetic fields

(51)

Detecting GW by CMB

GW propagating in isotropic electro-magnetic fields

(52)

hot

hot

cold

cold

cold cold

hot hot

Detecting GW by CMB

Space is stretched => Wavelength of light is also stretched

(53)

hot

hot

cold

cold

cold cold

hot hot

Detecting GW by CMB Polarisation

electron electron

Space is stretched => Wavelength of light is also stretched

(54)

hot

hot

cold

cold

cold cold

hot hot

Detecting GW by CMB Polarisation

Space is stretched => Wavelength of light is also stretched

54

(55)

horizontally polarised

Photo Credit: TALEX

(56)

Photo Credit: TALEX

(57)

Tensor-to-scalar Ratio

We really want to find this! The current upper bound is r<0.06 (95%CL)

r ⌘ h h ij h ij i h ⇣ 2 i

BICEP2/Keck Array Collaboration (2018)

(58)

WMAP(temp+pol)+ACT+SPT+BAO+H

0

WMAP(pol) + Planck + BAO ruled

out!

WMAP Collaboration

(59)

WMAP(temp+pol)+ACT+SPT+BAO+H

0

WMAP(pol) + Planck + BAO ruled

out!

ruled out!

ruled out!

ruled out!

ruled out!

Polarsiation limit added:

r<0.07 (95%CL)

Planck Collaboration (2015); BICEP2/Keck Array Collaboration (2016)

(60)

WMAP(temp+pol)+ACT+SPT+BAO+H

0

WMAP(pol) + Planck + BAO ruled

out!

ruled out!

ruled out!

ruled out!

ruled out!

Planck Collaboration (2015); BICEP2/Keck Array Collaboration (2016)

BICEP2/Keck Array Collaboration (2018)

r<0.06 (95%CL)

2018

Polarsiation limit added:

r<0.07 (95%CL)

(61)

Experimental

Landscape

(62)

What comes next?

Advanced Atacama Cosmology Telescope

South Pole Telescope “3G”

CLASS

BICEP/Keck Array

(63)

Advanced Atacama

Cosmology Telescope

(64)

South Pole Telescope “3G”

CLASS BICEP/Keck Array

CMB-S4(?)

(65)

CMB Stages

4

Detectors are a big challenge,

2000 2005 2010 2015 2020

10−4 10−3 10−2 10−1

WMAP

Planck

CMB

S4

Year

Approximate raw experimental sensitivity (µK)

Space based experiments Stage−I − ≈ 100 detectors Stage−II − ≈ 1,000 detectors Stage−III − ≈ 10,000 detectors Stage−IV − ≈ 100,000 detectors

Approximate raw experimental noiseK)

Figure by Clem Pryke for 2013 Snowmass documents

then

now

(66)

The Biggest Enemy:

Polarised Dust Emission

The upcoming data will NOT be limited by statistics, but by systematic effects such as the Galactic contamination

Solution: Observe the sky at multiple frequencies, especially at high frequencies (>300 GHz)

This is challenging, unless we have a superb, high- altitude site with low water vapour

CCAT-p!

(67)

CCAT-p Collaboration

(68)

Frank Bertoldi’s slide from the Florence meeting

(69)

Frank Bertoldi’s slide from the Florence meeting

Cornell U. + German consortium + Canadian consortium + …

(70)

A Game Changer

CCAT-p

: 6-m, Cross-dragone design, on Cerro Chajnantor (5600 m)

Germany makes great telescopes!

Design study completed, and the contract has been signed by

“VERTEX Antennentechnik GmbH”

CCAT-p is a great opportunity for Germany to make

significant contributions towards the CMB S-4 landscape (both US and Europe) by providing telescope designs and the “lessons learned” with prototypes.

(71)

Simons Observatory (USA)

in collaboration

South Pole?

(72)

Simons Observatory (USA)

in collaboration

South Pole?

This could be

“CMB-S4”

(73)

To have even more

frequency coverage…

(74)

ESA

2025– [proposed]

JAXA

LiteBIRD

2027– Selected!

+ participations from USA, Canada, Europe

Target: δr<0.001 (68%CL)

(75)

Polarized foregrounds

Synchrotron radiation and thermal emission from inter-galactic dust

Characterize and remove foregrounds

15 frequency bands between 40 GHz - 400 GHz

Split between Low Frequency Telescope (LFT) and High Frequency Telescope (HFT)

LFT: 40 GHz – 235 GHz

HFT: 280 GHz – 400 GHz

Foreground Removal

7

Polarized galactic emission (Planck X) LiteBIRD: 15 frequency bands

Slide courtesy Toki Suzuki (Berkeley)

(76)

LiteBIRD

LiteBIRD Spacecraft

LiteBIRD for B-mode from Space

2018/7/21 11

LFT (5K)

HG-antenna HFT (5K)

V-groove

radiators SVM/BUS

PLM 200K100K30K

JAXA

H3 LFT (Low frequency telescope) 34 – 161 GHz : Synchrotron + CMB HFT (high frequency telescope) 89 – 448 GHz : CMB + Dust

4.5 m

Focal plane 0.1K

Slide courtesy Yutaro Sekimoto (ISAS/JAXA)

European Contribution

(77)

LiteBIRD Collaboration

(78)

LiteBIRD Collaboration

(79)

Summary

Inflation looks pretty good: passed all the tests using the scalar (density) perturbation

Next frontier: Using CMB polarisation to find GWs from inflation. Critical test of the physics of inflation!

With CCAT-p, we can remove the dust polarisation to

reach r~10–2 reliably, i.e., 10 times better than the current bound

With LiteBIRD we plan to reach r~10–3, i.e., 100 times better than the current bound

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