Finding gravitational waves from the early Universe

(1)

Finding gravitational waves from the early Universe

Eiichiro Komatsu

[Max Planck Institute for Astrophysics]

IAS/PU Joint Astrophysics Colloquium

Princeton, October 1, 2019

(2)

(3)

(4)

Full-dome movie for planetarium Director: Hiromitsu Kohsaka

(5)

(6)

B-mode polarisation from gravitational lensing

E-mode polarisation from sound waves

Temperature from sound waves

B-mode from GW

(7)

Power spectrum, explained

(8)

B-mode from gravitational lensing E-mode

from sound waves

B-mode from GW

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

(9)

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 noise (µK)

Figure by Clem Pryke for 2013 Snowmass documents

then

now

(10)

E-mode

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!!

(11)

ESA

2025– [proposed]

JAXA

LiteBIRD

+ participations from USA, Canada, Europe

Polarisation satellite dedicated to measure CMB polarisation from

primordial GW, with a few thousand TES bolometers in space

2028–

(12)

ESA

2025– [proposed]

JAXA

LiteBIRD

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

We will go to L2!

+ participations from USA, Canada, Europe

Selected!

2028–

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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?

(15)

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)

(16)

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!

(17)

Inflationary 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)

(18)

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

•

^h^ij : “gravitational waves” (tensor mode)

•

Perturbation that does not alter the determinant

(19)

Measuring GW

d`

²

= dx

²

= X

ij

dx

ⁱ

dx

^j

d`

²

= X

ij

(

_ij

+ h

_ij

)dx

ⁱ

dx

^j

•

GW changes distances between two points

(20)

Laser Interferometer

Mirror

detector _{No signal}

(21)

Laser Interferometer

Mirror

Signal!

detector

(22)

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?

(23)

Detecting GW by CMB

Isotropic electro-magnetic fields

(24)

Detecting GW by CMB

GW propagating in isotropic electro-magnetic fields

h ⁺ _ij

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h ^⇥ _ij

<latexit sha1_base64="NwsD1SgjkJfMeVFacsNc7+DBIRA=">AAAB+HicbVBNS8NAEJ34WetHox69BIvgqSQi6LHoxWMF+wFtDZvtpl272YTdiVBDfokXD4p49ad489+4bXPQ1gcDj/dmmJkXJIJrdN1va2V1bX1js7RV3t7Z3avY+wctHaeKsiaNRaw6AdFMcMmayFGwTqIYiQLB2sH4euq3H5nSPJZ3OElYPyJDyUNOCRrJtysjP+MP+X3WQx4xnft21a25MzjLxCtIFQo0fPurN4hpGjGJVBCtu56bYD8jCjkVLC/3Us0SQsdkyLqGSmK29LPZ4blzYpSBE8bKlERnpv6eyEik9SQKTGdEcKQXvan4n9dNMbzsZ1wmKTJJ54vCVDgYO9MUnAFXjKKYGEKo4uZWh46IIhRNVmUTgrf48jJpndU8t+bdnlfrV0UcJTiCYzgFDy6gDjfQgCZQSOEZXuHNerJerHfrY966YhUzh/AH1ucPjLyTpw==</latexit><latexit sha1_base64="NwsD1SgjkJfMeVFacsNc7+DBIRA=">AAAB+HicbVBNS8NAEJ34WetHox69BIvgqSQi6LHoxWMF+wFtDZvtpl272YTdiVBDfokXD4p49ad489+4bXPQ1gcDj/dmmJkXJIJrdN1va2V1bX1js7RV3t7Z3avY+wctHaeKsiaNRaw6AdFMcMmayFGwTqIYiQLB2sH4euq3H5nSPJZ3OElYPyJDyUNOCRrJtysjP+MP+X3WQx4xnft21a25MzjLxCtIFQo0fPurN4hpGjGJVBCtu56bYD8jCjkVLC/3Us0SQsdkyLqGSmK29LPZ4blzYpSBE8bKlERnpv6eyEik9SQKTGdEcKQXvan4n9dNMbzsZ1wmKTJJ54vCVDgYO9MUnAFXjKKYGEKo4uZWh46IIhRNVmUTgrf48jJpndU8t+bdnlfrV0UcJTiCYzgFDy6gDjfQgCZQSOEZXuHNerJerHfrY966YhUzh/AH1ucPjLyTpw==</latexit><latexit sha1_base64="NwsD1SgjkJfMeVFacsNc7+DBIRA=">AAAB+HicbVBNS8NAEJ34WetHox69BIvgqSQi6LHoxWMF+wFtDZvtpl272YTdiVBDfokXD4p49ad489+4bXPQ1gcDj/dmmJkXJIJrdN1va2V1bX1js7RV3t7Z3avY+wctHaeKsiaNRaw6AdFMcMmayFGwTqIYiQLB2sH4euq3H5nSPJZ3OElYPyJDyUNOCRrJtysjP+MP+X3WQx4xnft21a25MzjLxCtIFQo0fPurN4hpGjGJVBCtu56bYD8jCjkVLC/3Us0SQsdkyLqGSmK29LPZ4blzYpSBE8bKlERnpv6eyEik9SQKTGdEcKQXvan4n9dNMbzsZ1wmKTJJ54vCVDgYO9MUnAFXjKKYGEKo4uZWh46IIhRNVmUTgrf48jJpndU8t+bdnlfrV0UcJTiCYzgFDy6gDjfQgCZQSOEZXuHNerJerHfrY966YhUzh/AH1ucPjLyTpw==</latexit><latexit sha1_base64="NwsD1SgjkJfMeVFacsNc7+DBIRA=">AAAB+HicbVBNS8NAEJ34WetHox69BIvgqSQi6LHoxWMF+wFtDZvtpl272YTdiVBDfokXD4p49ad489+4bXPQ1gcDj/dmmJkXJIJrdN1va2V1bX1js7RV3t7Z3avY+wctHaeKsiaNRaw6AdFMcMmayFGwTqIYiQLB2sH4euq3H5nSPJZ3OElYPyJDyUNOCRrJtysjP+MP+X3WQx4xnft21a25MzjLxCtIFQo0fPurN4hpGjGJVBCtu56bYD8jCjkVLC/3Us0SQsdkyLqGSmK29LPZ4blzYpSBE8bKlERnpv6eyEik9SQKTGdEcKQXvan4n9dNMbzsZ1wmKTJJ54vCVDgYO9MUnAFXjKKYGEKo4uZWh46IIhRNVmUTgrf48jJpndU8t+bdnlfrV0UcJTiCYzgFDy6gDjfQgCZQSOEZXuHNerJerHfrY966YhUzh/AH1ucPjLyTpw==</latexit>

(25)

hot

cold

cold cold

hot hot

Detecting GW by CMB

Space is stretched => Wavelength of light is also stretched

h ⁺ _ij

h ^⇥ _ij

(26)

hot

cold

cold cold

hot hot

Detecting GW by CMB Polarisation

electron electron

Space is stretched => Wavelength of light is also stretched

h ⁺ _ij

h ^⇥ _ij

(27)

hot

cold

cold cold

hot hot

Detecting GW by CMB Polarisation

Space is stretched => Wavelength of light is also stretched

h ⁺ _ij

27

h ^⇥ _ij

(28)

horizontally polarised

Photo Credit: TALEX

(29)

Photo Credit: TALEX

(30)

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

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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

<latexit sha1_base64="X8xOF/I7t8yOUTmoWj17kDkgmw4=">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</latexit><latexit sha1_base64="X8xOF/I7t8yOUTmoWj17kDkgmw4=">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</latexit><latexit sha1_base64="X8xOF/I7t8yOUTmoWj17kDkgmw4=">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</latexit><latexit sha1_base64="X8xOF/I7t8yOUTmoWj17kDkgmw4=">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</latexit>

scale-invariant spectrum

(31)

Propagation of GW

•

In an expanding Universe,

⇤ h _ij = 0

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gives

h ¨ _ij + 3 ˙ a

a h ˙ _ij + k ²

a ² h _ij = 16⇡ GT _ij ^GW

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expansion of the Universe aﬀects h

ij

=3H

(32)

GW Evolution

•

Super-horizon scales [k << aH]

•

The amplitude of GW is conserved (i.e., hij = constant)

•

Sub-horizon scales [k >> aH]

•

The amplitude of GW decays (i.e., hij ~ 1/a)

Therefore, the long-wavelength

GW preserves the initial condition:

the beginning of the Universe!

(33)

GW “entering the horizon”

•

This is a tricky concept, but it is important

•

Suppose that GWs were created at all wavelengths

•

As the Universe expands, the horizon size grows and we can see longer and longer wavelengths

•

Fluctuations “entering the horizon”

(34)

10 Gpc today 1 Gpc today 100 Mpc today

10 Mpc today 1 Mpc today

“enter the horizon”

Radiation Era Matter Era

a k

<latexit sha1_base64="0WH/fC7ApXueVifNR9Qec6YYzK0=">AAAB8nicbVBNS8NAEJ34WetX1aOXxSJ4KkkV9Fj04rGC/YA0lM120y7dbMLuRCihP8OLB0W8+mu8+W/ctjlo64OBx3szzMwLUykMuu63s7a+sbm1Xdop7+7tHxxWjo7bJsk04y2WyER3Q2q4FIq3UKDk3VRzGoeSd8Lx3czvPHFtRKIecZLyIKZDJSLBKFrJ70WaspxO8/G0X6m6NXcOskq8glShQLNf+eoNEpbFXCGT1Bjfc1MMcqpRMMmn5V5meErZmA65b6miMTdBPj95Ss6tMiBRom0pJHP190ROY2MmcWg7Y4ojs+zNxP88P8PoJsiFSjPkii0WRZkkmJDZ/2QgNGcoJ5ZQpoW9lbARtSmgTalsQ/CWX14l7XrNu6zVH66qjdsijhKcwhlcgAfX0IB7aEILGCTwDK/w5qDz4rw7H4vWNaeYOYE/cD5/ANqrkaA=</latexit>

(35)

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

(36)

Spectrum of GW today

Watanabe & EK (2006)

CMB PTA Interferometers

Wavelength of GW

~ Billions of light years!!!

Theoretical energy density

(37)

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)

(38)

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

0

WMAP(pol) + Planck + BAO ^ruled

out!

WMAP Collaboration

(39)

0

out!

ruled out!

Polarsiation limit added:

r<0.07 (95%CL)

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

(40)

0

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)

(41)

ESA

2025– [proposed]

JAXA

LiteBIRD

+ participations from USA, Canada, Europe

Selected!

2028–

Target: δr<0.001 (68%CL)

(42)

• 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)

(43)

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

(44)

LiteBIRD Collaboration

(45)

LiteBIRD Collaboration

(46)

But, wait a minute…

(47)

Are GWs from vacuum fluctuation in spacetime, or from sources?

•

Homogeneous solution: “GWs from vacuum fluctuation”

•

Inhomogeneous solution: “GWs from sources”

•

Scalar and vector fields cannot source tensor

fluctuations at linear order (possible at non-linear level)

•

SU(2) gauge field can!

⇤ h _ij = 16⇡ G⇡ _ij

Maleknejad & Sheikh-Jabbari (2013); Dimastrogiovanni & Peloso (2013);

Adshead, Martinec & Wyman (2013); Obata & Soda (2016); …

Many papers by Sorbo, Peloso, and others

(48)

Important Message

•

Do not take it for granted if someone told you that

detection of the primordial gravitational waves would be a signature of “quantum gravity”!

•

Only the homogeneous solution corresponds to the

vacuum tensor metric perturbation. There is no a priori reason to neglect an inhomogeneous solution!

•

Contrary, we have several examples in which detectable B-modes are generated by sources [U(1) and SU(2)]

⇤ h _ij = 16⇡ G⇡ _ij

(49)

Experimental Strategy

Commonly Assumed So Far

1. Detect CMB polarisation in multiple frequencies, to make sure that it is from the CMB (i.e., Planck spectrum)

2. Check for scale invariance: Consistent with a scale invariant spectrum?

•

Yes => Announce discovery of the vacuum fluctuation in spacetime

•

No => WTF?

(50)

New Experimental Strategy:

New Standard!

2. Consistent with a scale invariant spectrum?

3. Parity violating correlations consistent with zero?

4. Consistent with Gaussianity?

•

If, and ONLY IF Yes to all => Announce discovery of the vacuum fluctuation in spacetime

(51)

New Experimental Strategy:

New Standard!

2. Consistent with a scale invariant spectrum?

3. Parity violating correlations consistent with zero?

4. Consistent with Gaussianity?

•

If, and ONLY IF Yes to all => Announce discovery of the vacuum fluctuation in spacetime

If not, you may have just discovered new physics

during inflation!

(52)

Further Remarks

•

“Guys, you are complicating things too much!”

• ^No.

These sources (eg., gauge fields) should be

ubiquitous in a high-energy universe. They have every right to produce GWs if they are around

•

Sourced GWs with r>>0.001 can be phenomenologically more attractive than the vacuum GW from the large-field inflation [requiring super-Planckian field excursion]. Better radiative stability, etc

•

Rich[er] phenomenology: Better integration with the Standard Model; reheating; baryon synthesis via

leptogenesis, etc. Testable using many more probes!

(53)

GW from Axion-SU(2) Dynamics

•

φ: inflaton field => Just provides quasi-de Sitter background

•

χ: pseudo-scalar “axion” field. Spectator field (i.e., negligible energy density compared to the inflaton)

•

Field strength of an SU(2) field :

Dimastrogiovanni, Fasielo & Fujita (2017)

[I don’t want to touch this sector because I don’t understand inflaton]

[a=1,2,3; μ=0,1,2,3] self-interaction term

(54)

GW from Axion-SU(2) Dynamics

•

φ: inflaton field => Just provides quasi-de Sitter background

•

χ: pseudo-scalar “axion” field. Spectator field (i.e., negligible energy density compared to the inflaton)

•

Field strength of an SU(2) field :

Dimastrogiovanni, Fasiello & Fujita (2017)

[I don’t want to touch this sector because I don’t understand inflaton]

A well-defined set up:

Axion-SU(2) gauge field dynamics in a given de-Sitter background.

Everything is calculable!

self-interaction term [a=1,2,3; μ=0,1,2,3]

(55)

Background and Perturbation

•

In an inflating background, the SU(2) field has an

isotropic

background solution:

A ^a _i = [scale factor] ⇥ Q ⇥ _i ^a

U: axion potential

•

Perturbations contain a tensor (spin-2) mode (as well as S&V)

Maleknejad & Sheikh-Jabbari (2011)

A. Maleknejad (MPA)

(56)

Scenario

•

The SU(2) field contains 1 tensor, 2 vectors, and 3 scalars (9 DOF = 12 – 3)

•

The tensor components are amplified strongly by a coupling to the axion field

•

Only one helicity is amplified => GW is chiral (well- known result, also for U(1))

•

New result: GWs sourced by this mechanism are strongly non-Gaussian!

Agrawal, Fujita & EK, PRD, 97, 103526 (2018); JCAP 1806, 027 (2018)

(57)

Gravitational Waves

•

Defining canonically-normalised circular polarisation modes as

•

The equations of motion for L and R modes are

⇤ ^L,R 6 = 0

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(58)

Gravitational Waves

•

The equations of motion for L and R modes are ( )

= a few

(

spin-2 field

spin-2 field Dimastrogiovanni, Fasiello & Fujita (2017)

(59)

Spin-2 Field from SU(2)

•

The equations of motion for L and R modes of SU(2) are

the minus sign gives an instability -> exponential amplification of tR!

= a few

(

(60)

Spin-2 Field from SU(2)

•

The equations of motion for L and R modes of SU(2) are

[Whittaker function]

(

•

The produced gravitational waves are totally chiral!

•

The solution (when all the parameters are constant and the terms on the right hand side are ignored):

(61)

Gravitational Waves

•

The equations of motion for L and R modes are ( )

•

Inhomogeneous solution:

FE, FB: some complicated functions

(62)

•

This exponential dependence on mQ makes it possible to have Psourced >> Pvacuum

= (2/π

²

)H

²

/M

²Pl

• New Paradigm

Power Spectrum!

(63)

Phenomenology

•

The scale-dependence of the produced tensor modes is determined by how mQ changes with time

•

E.g., Axion rolling faster towards the end of inflation:

BLUE TILTED power spectrum! Therefore…

= a few

= …

(

(64)

Not just CMB!

Thorne, Fujita, Hazumi, Katayama, EK & Shiraishi, PRD, 97, 043506 (2018) LISA

BBO Planck

LiteBIRD

(65)

Example Tensor Spectra

Dimastrogiovanni, Fasiello & Fujita (2017) Thorne, Fujita, Hazumi, Katayama, EK & Shiraishi, PRD, 97, 043506 (2018)

•

Sourced tensor spectrum can also be bumpy

(66)

Example Tensor Spectra

Tensor Power Spectrum, P(k) B-mode CMB spectrum, ClBB

Dimastrogiovanni, Fasiello & Fujita (2017) Thorne, Fujita, Hazumi, Katayama, EK & Shiraishi, PRD, 97, 043506 (2018)

•

The B-mode power spectrum still looks rather normal

(67)

Parity-violating Spectra

•

Angle mis-calibration can be distinguished easily!

EB

TB

TB from angle

mis-calibration

Thorne, Fujita, Hazumi, Katayama, EK & Shiraishi, PRD, 97, 043506 (2018)

(68)

Large bispectrum in GW from SU(2) fields

•

^Ω^A << 1 is the energy density fraction of the gauge field

•

^B^h^/P^h2 is of order unity for the vacuum contribution

•

Gaussianity oﬀers a powerful test of whether the detected GW comes from the vacuum or sources

B _h ^RRR (k, k, k )

P _h ² (k ) ⇡ 25

⌦ _A

Aniket Agrawal (MPA)

Tomo Fujita (Kyoto)

[Maldacena (2003); Maldacena & Pimentel (2011)]

Agrawal, Fujita & EK, PRD, 97, 103526 (2018)

(69)

NG generated at the tree level

•

This diagram generates second-order equation of motion for GW

[GW]

[tensor SU(2)]

[mQ ~ a few]

~10

^–2

(70)

Result

•

This shape is similar to, but not exactly the same as, what was used by the Planck team to look for tensor bispectrum

k 3 /k 1

k 2 /k 1

(71)

Current Limit on Tensor NG

•

The Planck team reported a limit on the tensor bispectrum in the following form:

Planck Collaboration (2015)

f _NL ^tens ⌘ B _h ⁺⁺⁺ (k, k, k ) F _scalar ^equil. (k, k, k )

•

The denominator is the scalar equilateral bispectrum template, giving

F

_scalar^equil.

(k, k, k ) = (18/5)P

_scalar²

(k)

•

The current 68%CL constraint is

f

_NL^tens

= 400 ± 1500

(72)

LiteBIRD would nail it!

Courtesy of Maresuke Shiraishi

∆f

tens NL

in 1502.01592

tensor-to-scalar ratio r

RFG + LiteBIRD noise, 0% delens, f_sky = 0.5 noiseless, 100% delens, f_sky = 1 (∆f^tens_NL = 100r^3/2)

10^-1 10⁰ 10¹ 10²

10^-4 10^-3 10^-2 10^-1

50% sky, no delensing, LiteBIRD noise, and residual foreground

CV limited

Err[f

NLtens

] = a few!

(73)

Parameter Scan

Agrawal, Fujita & EK, JCAP, 97, 103526 (2018)

(74)

Schwinger Effect

Lozanov, Maleknejad & EK, arXiv:1805.09318

Kaloian Lozanov

(MPA) Azadeh Maleknejad

(MPA)

(75)

Summary

•

Next frontier: Using CMB polarisation to find primordial GW. Critical test of the physics of the early Universe!

•

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

•

GW from vacuum or sources? An exciting window to new physics

•

Check not only for scale invariant, but also for chirality and non-Gaussianity

(76)

Ground-based

Experiments

(77)

What comes next?

Advanced Atacama Cosmology Telescope

South Pole Telescope “3G”

CLASS

BICEP/Keck Array

(78)

Advanced Atacama

Cosmology Telescope

(79)

South Pole Telescope “3G”

CLASS BICEP/Keck Array

CMB-S4(?)

(80)

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!

(81)

CCAT-p Collaboration

(82)

Frank Bertoldi’s slide from the Florence meeting

(83)

Frank Bertoldi’s slide from the Florence meeting

Cornell U. + German consortium + Canadian consortium + …

(84)

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.

(85)

Simons Observatory (USA)

in collaboration

South Pole?

(86)

Simons Observatory (USA)

in collaboration

South Pole?

This could be

“CMB-S4”

(87)

SU(2), confronted

•

The SU(2) model of Dimastrogiovanni et al. predicts:

•

The current 68%CL constraint is

•

This is already constraining!

f

_NL^tens

Finding gravitational waves from the early Universe