Finding Cosmic Inflation - Eiichiro Komatsu MPI für Astrophysik Colloquium, MPI für Radioastronomie 24. Mai, 2019 - MPA
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Finding
Cosmic Inflation
Eiichiro Komatsu
[MPI für Astrophysik]
Colloquium, MPI für Radioastronomie
24. Mai, 2019
Full-dome movie for planetarium Director: Hiromitsu Kohsaka
Seven orders of magnitude in power
Temperature
from sound waves
in “just” 25 years
E-mode
from sound waves
B-mode from
gravitational lensing
B-mode from GW
Seven orders of magnitude in power
Temperature
from sound waves
in “just” 25 years
E-mode
from sound waves
B-mode from
gravitational lensing
B-mode from GW
We want this!!
Another two orders of magnitude
Temperature
from sound waves
in the next 10–15 years
E-mode
from sound waves
B-mode from
gravitational lensing
B-mode from GW
We want this!!
JAXA
+participations from
USA, Canada, Europe ESA
2025– [proposed]
LiteBIRD
2027– [proposed]
Polarisation satellite dedicated to
measure CMB polarisation from
primordial GW, with a few thousand
TES bolometers in space
JAXA
+participations from
USA, Canada, Europe ESA
2025– [proposed]
LiteBIRD
2027– Selected!
May 21: JAXA has chosen LiteBIRD
as the strategic large-class mission.
We will go to L2!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?
Mukhanov & Chibisov (1981); Hawking (1982); Starobinsky (1982); Guth & Pi (1982);
Bardeen, Turner & Steinhardt (1983)
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?Starobinsky (1980); Sato (1981); Guth (1981); Linde (1982); Albrecht & Steinhardt (1982)
Cosmic Inflation
Quantum fluctuations on
microscopic scales
Inflation!
• Exponential expansion (inflation) stretches the wavelength
of quantum fluctuations to cosmological scalesKey Predictions
ζ
scalar
• Fluctuations we observe today in CMB and the matter
distribution originate from quantum fluctuations during
inflation
Mukhanov&Chibisov (1981)
Guth & Pi (1982)
mode Hawking (1982)
Starobinsky (1982)
Bardeen, Steinhardt&Turner
hij
(1983)
• There should also be ultra long-wavelength
gravitational waves generated during inflation
Grishchuk (1974)
tensor Starobinsky (1979)
modeWe measure distortions in space
• A distance between two points in space
2 2 i j
d` = a (t)[1 + 2⇣(x, t)][ ij + hij (x, t)]dx dx
• 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
X
hii = 0
iWe measure distortions in space
• A distance between two points in space
2 2 i j
d` = a (t)[1 + 2⇣(x, t)][ ij + hij (x, t)]dx dx
scale factor
• 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
X
hii = 0
iFinding Inflation
• Inflation is the accelerated, quasi-exponential expansion.
Defining the Hubble expansion rate as H(t)=dln(a)/dt, we
must find
ä 2 Ḣ
= Ḣ + H > 0 ✏⌘ < 1
a H2
• 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:
Z tend
aend 0 0
N ⌘ ln = dt H(t ) ⇡ 50
a tHave we found inflation?
Ḣ
• Have we found εFluctuations 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 anglesFluctuations 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 powerData Analysis • Decompose temperature fluctuations in the sky into a set of waves with various wavelengths • Make a diagram showing the strength of each wavelength
WMAP Collaboration
Amplitude of Waves [μK2]
Long Wavelength Short Wavelength
180 degrees/(angle in the sky)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 soupMeasuring Abundance of H&He
Long Wavelength Short Wavelength
[μK ]
2
Amplitude of Waves
180 degrees/(angle in the sky)Measuring Total Matter Density
Long Wavelength Short Wavelength
[μK ]
2
Amplitude of Waves
180 degrees/(angle in the sky)Origin of Fluctuations
• Who dropped those Tofus into the cosmic Miso
soup?Amplitude of Waves [μK2]
Long Wavelength Short Wavelength
Removing Ripples:
Power Spectrum of
Primordial Fluctuations
180 degrees/(angle in the sky)Amplitude of Waves [μK2]
Long Wavelength Short Wavelength
Removing Ripples:
Power Spectrum of
Primordial Fluctuations
180 degrees/(angle in the sky)Amplitude of Waves [μK2]
Long Wavelength Short Wavelength
Removing Ripples:
Power Spectrum of
Primordial Fluctuations
180 degrees/(angle in the sky)Amplitude of Waves [μK2]
Long Wavelength Short Wavelength
Let’s parameterise like
ns 1
Wave Amp. / `
180 degrees/(angle in the sky)Amplitude of Waves [μK2] Wright, Smoot, Bennett & Lubin (1994)
Long Wavelength Short Wavelength
In 1994:
1989–1993
COBE 2-Year Limit!
ns=1.25 –0.45 (68%CL)
+0.4
ns 1
Wave Amp. / `
l=3–30
180 degrees/(angle in the sky)WMAP Collaboration
Amplitude of Waves [μK2]
20 years later…
Long Wavelength Short Wavelength
2001–2010
WMAP 9-Year Only:
ns=0.972±0.013 (68%CL)
ns 1
Wave Amp. / `
180 degrees/(angle in the sky)WMAP Collaboration
Amplitude of Waves [μK2]
2001–2010 South Pole Telescope
[10-m in South Pole]
1000
ns=0.965±0.010
Atacama Cosmology Telescope
[6-m in Chile]
100WMAP Collaboration
Amplitude of Waves [μK2]
2001–2010 South Pole Telescope
[10-m in South Pole]
1000
ns=0.961±0.008
~5σ discovery of ns[μK2] 2009–2013
Planck 2013 Result!
Waves
ns=0.960±0.007
First >5σ discovery of nsFraction of the Number of Pixels
Having Those Temperatures
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 WMAP Collaboration
Having Those Temperatures
Histogram: WMAP Data
Red Line: Gaussian
YES!!
[Values of Temperatures in the Sky Minus 2.725 K] / [Root Mean Square]Testing Gaussianity
Fraction of the Number of Pixels
• Since a Gauss distribution
Having Those Temperatures
is symmetric, it must yield a
vanishing 3-point function
Z 1
3 3
h T i⌘ d T P( T) T
1
Histogram: WMAP Data • More specifically, we measure
Red Line: Gaussian this by averaging the product
of temperatures at three
different locations in the sky
[Values of Temperatures in the Sky Minus
2.725 K]/ [Root Mean Square] h T (n̂1 ) T (n̂2 ) T (n̂3 )iLack 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)
3 2
⇣(x) = ⇣gaus (x) + fNL ⇣gaus (x) with fNL = 37 ± 20 (68% CL)
5
WMAP 9-year Result
• The Planck data improved the upper bound by an order of
magnitude: deviation isSo, have we found inflation?
• Single-field slow-roll inflation looks remarkably good:
• Super-horizon fluctuation
• Adiabaticity
• Gaussianity
• nsGrishchuk (1974); Starobinsky (1979)
Gravitational waves as the quantum
vacuum fluctuation in spacetime
• Quantising the gravitational waves in de Sitter
space in vacuum
⇤hij = 0
AAAB+HicbVBNSwMxEJ31s9aPrnr0EiyCp7Irgl6EUi8eK9gPaJclm6ZtbDZZkqxYl/4SLx4U8epP8ea/MW33oK0PBh7vzTAzL0o408bzvp2V1bX1jc3CVnF7Z3ev5O4fNLVMFaENIrlU7QhrypmgDcMMp+1EURxHnLai0fXUbz1QpZkUd2ac0CDGA8H6jGBjpdAtdWvyEQ3DjN1P0BXyQrfsVbwZ0DLxc1KGHPXQ/er2JEljKgzhWOuO7yUmyLAyjHA6KXZTTRNMRnhAO5YKHFMdZLPDJ+jEKj3Ul8qWMGim/p7IcKz1OI5sZ4zNUC96U/E/r5Oa/mWQMZGkhgoyX9RPOTISTVNAPaYoMXxsCSaK2VsRGWKFibFZFW0I/uLLy6R5VvG9in97Xq7W8jgKcATHcAo+XEAVbqAODSCQwjO8wpvz5Lw4787HvHXFyWcO4Q+czx8805Il
gives
3 ij⇤ 0
k hhij (k)h (k )i
scale-invariant spectrum
✓ ◆2
3 0 8 H
= (2⇡) D (k k) 2
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
Mpl 2⇡Watanabe & EK (2006)
Theoretical energy density
Spectrum of GW today
GW entered the horizon during
the matter era
GW entered the horizon during
the radiation eraWatanabe & EK (2006)
Theoretical energy density
Spectrum of GW today
CMB PTA Interferometers
Wavelength of GW
~ Billions of light years!!!Measuring GW
• GW changes distances between two points
X
2 2 i j
d` = dx = ij dx dx
ij
X
2 i j
d` = ( ij + hij )dx dx
ijLaser Interferometer
Mirror
Mirror
detector No signalLaser Interferometer
Mirror
Mirror
detector Signal!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?Detecting GW by CMB Isotropic electro-magnetic fields
Detecting GW by CMB GW propagating in isotropic electro-magnetic fields
Detecting GW by CMB
Space is stretched => Wavelength of light is also stretched
ld
co
hot
ho
t
cold
cold
ho
hot
t
ld
coDetecting GW by CMB
Polarisation
Space is stretched => Wavelength of light is also stretched
ld
co
hot
ho
t
cold
electron cold electron
ho
hot
t
ld
coDetecting GW by CMB
Polarisation
Space is stretched => Wavelength of light is also stretched
ld
co
hot
ho
t
cold
cold
ho
hot
t
ld
co
54Photo Credit: TALEX
horizontally polarisedPhoto Credit: TALEX
Tensor-to-scalar Ratio
ij
hhij h i
r⌘ 2
h⇣ i
• We really want to find this! The current upper bound is
rWMAP Collaboration
WMAP(temp+pol)+ACT+SPT+BAO+H0
WMAP(pol) + Planck + BAO ruled
out!Planck Collaboration (2015); BICEP2/Keck Array Collaboration (2016)
Polarsiation limit added:
WMAP(temp+pol)+ACT+SPT+BAO+H 0
WMAP(pol)
rPlanck Collaboration (2015); BICEP2/Keck Array Collaboration (2016)
Polarsiation limit added:
WMAP(temp+pol)+ACT+SPT+BAO+H 0
WMAP(pol)
rExperimental Landscape
Advanced Atacama South Pole Telescope “3G”
Cosmology Telescope
What comes next?
BICEP/Keck Array CLASSAdvanced Atacama Cosmology Telescope
South Pole Telescope “3G” CMB-S4(?) BICEP/Keck Array CLASS
CMB Stages
Space based experiments
−1
Detectors are a big challenge, Stage−I − ≈ 100 detectors
(µK)
10
noise(µK)
Stage−II − ≈ 1,000 detectors
Stage−III − ≈ 10,000 detectors
W Stage−IV − ≈ 100,000 detectors
sensitivity
M
AP
experimental
−2
10
rawexperimental
then
Pl
an
ck now
Approximate raw
−3
10
Approximate
CM
B−
S4
−4
10
2000 2005 2010 2015 2020
Year
Figure by Clem Pryke for 2013 Snowmass documents 4The 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!CCAT-p Collaboration
Frank Bertoldi’s slide from the Florence meeting
Frank Bertoldi’s slide from the Florence meeting Cornell U. + German consortium + Canadian consortium + …
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.Simons Observatory
(USA)
in collaboration
South Pole?This could be
“CMB-S4”
Simons Observatory
(USA)
in collaboration
South Pole?To have even more frequency coverage…
JAXA
+participations from
USA, Canada, Europe ESA
2025– [proposed]
LiteBIRD
2027– Selected!
Target: δrForeground Removal
Polarized galactic emission (Planck X) LiteBIRD: 15 frequency bands
• 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 Slide courtesy Toki Suzuki (Berkeley)
7Slide courtesy Yutaro Sekimoto (ISAS/JAXA)
LiteBIRD Spacecraft
LiteBIRD
JAXA
H3 LFT (Low frequency telescope) 34 – 161 GHz : Synchrotron + CMB
HFT (high frequency telescope) 89 – 448 GHz : CMB + Dust
4.5 m
European Contribution
LFT (5K)
HFT (5K)
Focal plane 0.1K
V-groove PLM
30K
100K
200K radiators
SVM/BUS
HG-antenna
2018/7/21 LiteBIRD for B-mode from Space 11LiteBIRD Collaboration
LiteBIRD Collaboration
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 boundYou can also read
