Chin Yu Lecture at National Taiwan University

1. The Past, Present and Future of
COSMOLOGY
Chin Yu Lecture
March 2021
Daniel Baumann
University of Amsterdam &
National Taiwan University

2. “Our universe is SIMPLE, but STRANGE.”
David Spergel

3. ⌦b Amount of ordinary matter
⌦m Amount of dark matter
⌦⇤ Amount of dark energy Age of the universe
It is SIMPLE, because just 5 parameters describe all observations:
As
ns
Amplitude of density fluctuations
Scale dependence of the fluctuations

4. It is STRANGE, because we don’t understand these parameters:
⌦b
⌦m
⌦⇤
Why is there more matter than antimatter?
What is the dark matter?
What is the dark energy?
As
ns
What was the origin of the fluctuations?

5. Outline of this talk:
The Past
How did we get here?
The Present
What does it all mean?
The Future
How can we find out?

6. The Past

7. The Expanding Universe
0 0.5 1 1.5 2
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
×103
Distance [Mpc]
Velocity
[km/sec]
0 5 10 15 20 25 30 35
0
5
10
15
20
×103
Distance [Mpc]
Modern cosmology began with Hubble’s discovery of the expansion of the
universe:
Hubble (1929)
Hubble and Hummerson (1932)

8. The universe therefore started in a hot and dense state:
As the universe expands, it cools.
temperature
earlier later
time
hotter colder

9. t=10μs: Quarks and gluons condense into nuclei:
temperature
time
u
d
u
u
d
d
proton
neutron
10 μs

10. t=1s: Neutrinos decouple and neutrons freeze out:
temperature
time
1 s
Free-streaming neutrinos
• 40% of the energy density
• Significant effect on the expansion

11. t=3min: Light elements (H, He, and Li) form:
temperature
time
H He
3 min

12. 380,000 yrs
e-
e-
e-
e-
e-
e-
H He
e
temperature
time
t=380,000yrs: Atoms form and the first light is released:
Free-streaming
photons

13. • 410 photons per cubic centimeter
• cooled by the expansion: 2.7 K
• faint microwave radiation: CMB
This afterglow of the Big Bang is still seen today:
0
100
200
300
400
Intensity
[MJy/sr]
100 200 300 400 500 600
−0.1
0
0.1
Frequency [GHz]

14. temperature
time
t>1billionyrs: Matter collapses into stars and galaxies:
1 billion yrs

15. This history of the universe is an observational fact:
10 μs 380,000 yrs
1 s 3 min
QCD phase
transition
Neutrino
decoupling
BBN
e
-
Photon
decoupling
Structure
formation
1 billion yrs
• The basic picture has been confirmed by many independent observations.
• Many precise details are probed by measurements of the CMB.

16. CMB Anisotropies
The CMB has tiny temperature variations that reflect perturbations in the
density of the primordial plasma:
WMAP
COBE Planck
1992
2001-2010
2013-2017

17. The fluctuations aren’t random, but are correlated over large distances:
These correlations contains an enormous amount of information about the
physics of the early universe.
2 10 30
0
1000
2000
3000
4000
5000
6000
Power
[µK
2
]
500 1000 1500 2000 2500
Multipole
90◦
18◦ 1◦
0.2◦
0.1◦
0.07◦
Angular separation

18. Figure courtesy of Mathew Madhavacheril
10 100 1000
Multipole

19. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

20. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

21. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

22. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

23. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

24. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

25. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

26. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

27. 10 100 1000
Multipole Figure courtesy of Mathew Madhavacheril

28. Fluctuations in the early universe propagate as sound waves:

29. Fluctuations in the early universe propagate as sound waves:
Dark matter
Photons + baryons
rs

30. Fluctuations in the early universe propagate as sound waves:

31. Temperature Polarization
These waves are imprinted in the pattern of CMB fluctuations:
2 +2
1 +1
0 2 +2
1 +1
0
20
40
60
80
0
0.4
0.2
0.0
0.2
0.4
intensity of 11396 cold spots
✓s ✓s
1
2 ✓s
Planck (2015)

32. 2 10 30
0
1000
2000
3000
4000
5000
6000
Power
[µK
2
]
500 1000 1500 2000 2500
Multipole
The power spectrum is the Fourier transform of these patterns:
The features of the spectrum allow us to measure the cosmological parameters.
✓s

33. Dark Matter
Without dark matter, the data would look very different:
Figures courtesy of Zhiqi Huang and Dick Bond [ACT collaboration]
Data No Dark Matter

34. This can also be seen in the power spectrum: ⌦m = 0.32 Planck (2018)
without dark matter
2 10 30
0
2000
4000
6000
8000
10000
Power
[µK
2
]
500 1000 1500 2000
Multipole

35. Dark Energy
Without dark energy, the data would look very different:
Data No Dark Energy
Figures courtesy of Zhiqi Huang and Dick Bond [ACT collaboration]

36. 2 10 30
0
1000
2000
3000
4000
5000
6000
Power
[µK
2
]
500 1000 1500 2000
Multipole
This can also be seen in the power spectrum: ⌦⇤ = 0.68
*
* Breaking a geometric degeneracy requires additional datasets (e.g. BAO).
Planck (2018)
without dark energy
with dark energy

37. with
dark energy
without
dark energy
Riess et al (1998)
Perlmutter et al (1998)
Direct evidence for dark energy comes from supernova observations:

38. Baryons
The peak heights depend on the baryon density: ⌦b = 0.04 Planck (2018)
The measured baryon density is consistent with BBN.
more baryons
2 10 30
0
1000
2000
3000
4000
5000
6000
7000
8000
Power
[µK
2
]
500 1000 1500 2000
Multipole

39. As
✓
k
k0
◆ns 1
Initial Conditions
The CMB power spectrum also probes the initial conditions:
A B C D
A
B
C
D
Amplitude
scale-dependence
As = 2.20 ⇥ 10 9
evolution

40. ns = 0.96
The primordial power spectrum is close to scale invariant:
WMAP (2009)
Planck (2018)
2 10 30
0
1000
2000
3000
4000
5000
6000
7000
Power
[µK
2
]
500 1000 1500 2000
Multipole
ns = 0.75
ns = 1.25
The observed deviation from scale invariance is significant.

41. The Standard Model
A simple 5-parameter model fits all observations:
Amount of ordinary matter
Amount of dark matter
Amount of dark energy
Amplitude of density fluctuations
Scale dependence of the fluctuations
⌦b = 0.04
ns = 0.96
109
As = 2.20
⌦⇤ = 0.68
⌦m = 0.32

42. The key challenge of modern cosmology is to explain these numbers:
Why is there more matter than antimatter?
What is the dark matter?
What is the dark energy?
⌦b
⌦m
⌦⇤
As
ns
What was the origin of the fluctuations?

43. The Present

44. As
ns
What was the origin of the fluctuations?
Each of the problems of the standard model deserves its own discussion.
In the rest of this talk, I will focus on the problem of the initial conditions:

45. 90◦
18◦
0
1000
2000
3000
4000
5000
6000
Power
[µK
2
]
2◦
0.2◦
0.1◦
0.07◦
Angular separation
An Important Clue
The correlations in the CMB span superhorizon scales:
Superhorizon

46. The Horizon Problem
distance light travelled
since the Big Bang
Photon
decoupling
This apparent conflict with causality is called the horizon problem:
2

47. The correlations must have been created before the hot Big Bang:
Big Bang
?
Photon
decoupling
distance light travelled
since the Big Bang

48. Inflation solves the problem by invoking a period of superluminal expansion:
Big Bang
Guth (1980)
Linde (1982)
Albrecht and Steinhardt (1982)
Inflation
Photon
decoupling

49. Inflation
In less than 10-32 seconds, the universe doubles in size at least 80 times:
The entire observable universe then originated from a microscopic, causally
connected region of space.
a(t) = eHt

50. To achieve this requires a substance with nearly constant energy density:
We don’t know what this substance is.
V ( )
The dynamics is described by
Inflation occurs if the evolution is dominated by the Hubble friction.
¨ + 3H ˙ =
dV
d
H2
⇡ V/(3M2
pl)

51. Quantum Fluctuations
Quantum fluctuations get amplified and stretched to macroscopic scales:
The correlations observed in the CMB are inherited from the correlations of
these quantum fluctuations.

52. The fluctuations during inflation satisfy
¨ + 3H ˙ +
k2
a2
= 0
This is the equation of a damped harmonic oscillator.
hx2
i =
~
2!
k3
2⇡2
h( )2
i =
k3
a3
~
2(k/a)
• At horizon crossing, this becomes
P (k) =
✓
H
2⇡
◆2
k/a=H
• The zero-point fluctuations of this oscillator are
H 1
x(t)

53. ! ⇢
The power spectrum of density fluctuations after inflation then is
P ⇢(k) =
✓
H
˙
◆2 ✓
H
2⇡
◆2
k/a=H
Mukhanov and Chibisov (1980)
Bardeen, Steinhardt and Turner (1982)
Starobinsky (1982)
Hawking (1982)
conversion
⌘ As
✓
k
k0
◆ns 1
: time translation invariance during inflation
• ns ⇡ 1
ns < 1
• : decay of the inflationary energy density

54. Current Evidence for Inflation
• homogeneous
• isotropic
• spatially flat
The universe is with fluctuations that
•span superhorizon scales
•are adiabatic
•have coherent phases
•are nearly scale invariant
•are very Gaussian
All of these features are naturally explained by inflation.
Are we done?

55. Current Evidence for Inflation
The universe is with fluctuations that
•span superhorizon scales
•are adiabatic
•have coherent phases
•are nearly scale invariant
•are very Gaussian
Although the evidence for inflation is growing, the physical origin of the
inflationary expansion remains a mystery.
What is the physics of inflation?
All of these features are naturally explained by inflation.
Are we done?
• homogeneous
• isotropic
• spatially flat

56. How can inflation become part of the standard history of
the universe with the same level of confidence as BBN ?
“Extraordinary claims require extraordinary evidence”
Carl Sagan
10 μs 1 s 3 min
QCD phase
transition
Neutrino
decoupling
BBN
10-32 s
Inflation?

57. The Future

58. Primordial Gravitational Waves
The strength of the signal depends on the energy scale of inflation, which
may be as high as 1016 GeV.
Besides density fluctuations, inflation predicts gravitational waves:

59. The strength of these higher-point correlations (non-Gaussianity) depends
on the type of substance that created inflation and its interactions.
Primordial Interactions
See my seminar next week.
Inflation also predicts correlations between more than just two points:

60. LIGO detected GWs with wavelengths
of order thousands of kilometers
The GWs produced by inflation have
wavelengths of order billions of light-years.
How do we detect them?

61. CMB Polarization
Gravitational waves produce CMB polarization:
Hot
Hot
Cold
Cold
Electron
Polarization
Polnarev (1985)

62. Density fluctuations also produce polarization, but the pattern is different:
E-modes
isotropic stretching of space anisotropic stretching of space
cold
B-modes
Density Perturbations
vs.
Gravitational Waves
Zaldarriaga and Seljak (1996)
Kamionkowski, Kosowsky and Stebbins (1996)

63. PSfrag
replacements
-160 160 µK
0.41 µK
+160
160
The observed CMB is indeed polarized
DASI (2002)
WMAP (2009)
Planck (2013)

64. Planck (2018)
The pattern is consistent with pure E-modes:
500 1000 1500 2000
Multipole
°150
°100
°50
0
50
100
150
Power
[µK
2
]
TE
500 1000 1500 2000
Multipole
0
10
20
30
40
50
EE
Curl-free E-mode pattern
cold

65. A few years ago, the BICEP collaboration announced that it had seen the elusive
B-modes:
Unfortunately, the signal was not primordial, but came from galactic dust.
BICEP (2014)
Right ascension [deg.]
Declination
[deg.]
−50
0
50
−65
−60
−55
−50
−0.3
0
0.3
B-mode signal

66. 10 100 1000
Multipole
10°4
10°3
10°2
10°1
100
101
102
103
104
Power
[µK
2
] T
E
B
Lensing
Primordial
The expected B-mode signal is small:

67. However, observations are getting remarkably sensitive:
10 100 1000
Multipole
10°4
10°3
10°2
10°1
Power
[µK
2
]
BICEP
SPTpol
Polarbear

68. 0.94 0.95 0.96 0.97 0.98 0.99
0
0.05
0.1
0.15
m2φ2
R2
1 − cos(φ/f)
ns
(r)
The data is starting to become really interesting
r < 0.07
Ruled out
Favored

69. Ongoing Experiments
EBEX
SPIDER
POLARBEAR
BICEP
SPTPol
ACTPol
ABS
CLASS
CMB Stage III

70. Planned Experiments
CMB Stage III.5
(2021-2028)
Atacama Desert

71. Planned Experiments
CMB Stage IV
(2028-2035)
Atacama Desert
South Pole

72. Planned Experiments
Selected by JAXA in 2019
Launch in 2028
LiteBIRD
(r) ⇠ 0.001

73. 380,000 yrs 1 billion yrs
10-32 s
A B-mode detection would be a milestone towards a complete
understanding of the origin of all structure in the universe
1014 GeV 1 eV 1 meV

74. Conclusions

75. ⌦b
Yet, many fundamental questions remain:
• What is dark matter and dark energy?
• Did inflation occur? And what was driving it?
• What is the origin of the matter-antimatter asymmetry?
• …
We hope that future observations will shed light on these questions.
Observations of the cosmic microwave background have revolutionized
cosmology:
⌦m
⌦⇤
As , ns

76. Thank you for your attention!

77. “I did not continue with studying the CMB, because I
had trouble imagining that such tiny disturbances to
the CMB could be detected ...”
Jim Peebles
“I thought that it would take 1000 years to detect the
logarithmic dependence of the power spectrum.”
Slava Mukhanov
ns = 0.960 ± 0.007
Lessons from the Past

78. “We apologise to experimentalists for having no idea what is the mass of the
Higgs boson and for not being sure of its couplings to other particles. For
these reasons we do not want to encourage big experimental searches for
the Higgs boson, …” Ellis, Gaillard and Nanopoulos
110 120 130 140 150
0
500
1000
1500
Data
S+B Fit
B Fit Component
Mass
Events
Lessons from the Past

79. “I arrived at the interesting result that
gravitational waves do not exist, …”
Einstein, in a letter to Born
Lessons from the Past