From the Big Bang to Dark Energy Outline 4. Infla1on and Dark Energy
From the Big Bang to Dark Energy Hitoshi Murayama Kavli IPMU, University of Tokyo UC Berkeley, Lawrence Berkeley Laboratory
1 Credit: NASA
How did the Universe begin? What is its fate? What is it made of? What are its fundamental laws? Where do we come from? Now in the realm of science!
Credit:(aNGeLic!(by(Rolfe(Kolbe( h7p://www.flickr.com/photos/46210293@N08/8287418426/(
2
Outline 1. From daily life to Big Bang 2. Birth of elements and Higgs boson 3. Dark matter and anti-matter 4. Inflation and Dark energy
3
4. Infla?on and Dark Energy
4
Infla?on
Credit: NASA
5
8B
13.
rs ky 380
yrs
in 3m ec th s lion -bil ten sec nth illio
1 tr
Higgs DM
CMB
Credit: C. Amsler et al. (Par?cle Data Group), Physics LeIers B667, 1 (2008)
6
yrs
rs ky
8B
13.
380
in 3m ec th s lion -bil ten sec nth illio 1 tr Higgs DM
CMB
Credit: C. Amsler et al. (Par?cle Data Group), Physics LeIers B667, 1 (2008)
6 A one million mark note used as a notepad
Credit: Bundesarchiv, Bild 183-‐R1215-‐506, CC BY-‐SA 3.0
Credit: Bundesarchiv, Bild 102-‐00193, CC BY-‐SA 3.0
Credit: Bundesarchiv, Bild 102-‐00104 / Pahl, Georg, CC BY-‐SA 3.0
Notes used as wallpaper
Hundred billion mark note
7
Credit: Dr Graham Beards, CC BY 3.0
Credit: NASA
8
Credit: Dr Graham Beards, CC BY 3.0
Credit: NASA
8
Credit: Dr Graham Beards, CC BY 3.0
>1026
Credit: NASA
8
Why do they all look the same?
• Like having discovered two
remote islands in very different parts of the world, speaking the same language
• even the accents are nearly the same: one part in 100,000
• we suspect they had Credit: NASA
communication
9
10
11 fly-‐by simula?on based on real data
Credit: Sloan Digital Sky Survey
12 fly-‐by simula?on based on real data
Credit: Sloan Digital Sky Survey
about ten trillion ?mes faster than light
12
fly-‐by simula?on based on real data
Credit: Sloan Digital Sky Survey
about ten trillion ?mes faster than light prac?cally the same no maIer how far you go
12
more or less uniform small winkles
2 billion light years
Credit: Sloan Digital Sky Survey
13
equa?on for cosmic expansion m
R M
14
equa?on for cosmic expansion m
R M
14
equa?on for cosmic expansion F = ma
m
R M
14
equa?on for cosmic expansion F = ma
F =
G
Mm R2
m
R M
14
equa?on for cosmic expansion F = ma
F = a=
G
Mm R2
d2 R dt2
m
R M
14
equa?on for cosmic expansion F = ma
F = a=
G
Mm R2
d2 R dt2
m
R M
2
M d R = −G 2 R dt 2
14
equa?on for cosmic expansion F = ma
F =
G
Mm R2
m
R
d2 R dt2
a=
M
2
M d R = −G 2 R dt 2 "=
1 2
✓
dR dt
◆2
G
M R
14
equa?on for cosmic expansion F = ma
F =
G
Mm R2
m
R
d2 R dt2
a=
M
2
M d R = −G 2 2 R dt conserved ✓ ◆2 "=
dR dt
1 2
G
M R
14
equa?on for cosmic expansion F = ma
F =
G
Mm R2
m
R
d2 R dt2
a=
M
2
M d −G 2 2R = R dt conserved ✓ ◆2 "=
1 2
dR dt
G
M =0±0.01 R
14
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M R =0
R M
15
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M =0 R
in terms of mass density ρ
R M
15
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M =0 R
in terms of mass density ρ M=
4⇡ 3 ⇢R 3
R M
15
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M =0 R
in terms of mass density ρ M=
R˙ R
!2
4⇡ 3 ⇢R 3
=
R M
8⇡ G⇢ 3
15
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M R =0
in terms of mass density ρ M=
R˙ R
!2
4⇡ 3 ⇢R 3
=
R M
8⇡ G⇢ 3
Friedmann equa?on
15
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
R M
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ
R M
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ 3
R M
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ =const 3
R M
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ =const 3
R M
dR = HR dt
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ =const 3
R M
dR = HR dt
R(t) = R(0) e Ht
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ =const 3
R M
dR = HR dt
R(t) = R(0) e Ht Universe expands exponen?ally!
16
17
constant energy per volume
1
17
constant energy per volume
1
8
17
constant energy per volume
1
8
total energy keeps growing like volume R(t)3∝e3Ht
17
constant energy per volume
1
8
total energy keeps growing like volume R(t)3∝e3Ht energy grows like volume makes the expansion faster energy grows even more
17
Ul?mate Free Lunch! constant energy per volume
1
8
total energy keeps growing like volume R(t)3∝e3Ht energy grows like volume makes the expansion faster energy grows even more
17
Ul?mate Free Lunch! constant energy per volume
1
8
total energy keeps growing like volume R(t)3∝e3Ht energy grows like!!volume makes the expansion faster energy grows even more
17
catch: Uncertainty Principle
18
physics is uncertain
Credit: © Hitachi, Ltd. 1994, 2013. All rights reserved.
Akira Tonomura
19
physics is uncertain
Credit: © Hitachi, Ltd. 1994, 2013. All rights reserved.
Akira Tonomura
19
interference of waves
a par?cle is a wave a wave is a par?cle
20
interference of waves
a par?cle is a wave a wave is a par?cle
20
quantum mechanics • law of physics at subatomic scales • uncertainty principle • you can’t predict what happens each time • but over time you find a regular pattern • a particle is a wave • a wave is a particle • when squeezed into narrow
Credit: Armedblowfish, BSD
space, wave is amplified
21
quantum mechanics • law of physics at subatomic scales • uncertainty principle • you can’t predict what happens each time • but over time you find a regular pattern • a particle is a wave • a wave is a particle • when squeezed into narrow
Credit: Armedblowfish, BSD
space, wave is amplified
21
quantum mechanics • law of physics at subatomic scales • uncertainty principle • you can’t predict what happens each time • but over time you find a regular pattern • a particle is a wave • a wave is a particle • when squeezed into narrow
Credit: Armedblowfish, BSD
space, wave is amplified
21
near sighted • What you are seeing one
moment is gone by inflation the next moment
• feel very near-sighted • “horizon” ≈ H • small space I
–1
⇒big uncertainty
22
near sighted • What you are seeing one
moment is gone by inflation the next moment
• feel very near-sighted • “horizon” ≈ H • small space I
–1
⇒big uncertainty
22
near sighted • What you are seeing one
moment is gone by inflation the next moment
• feel very near-sighted • “horizon” ≈ H • small space I
–1
⇒big uncertainty
22
vacuum is ac?ve
Quantum Chromodynamics movies are provided at hNp://www.physics.adelaide.edu.au/theory/ staff/leinweber/VisualQCD/Nobel/
23
seed for diversity • universe was born tiny • entire visible universe was • • •
smaller than 10–26 cm ripples were made by uncertain principle only 1mm ripple on 100m deep ocean ripples get stretched to macroscopic size
24
seed for diversity • universe was born tiny • entire visible universe was • • •
Credit: NASA
smaller than 10–26 cm ripples were made by uncertain principle only 1mm ripple on 100m deep ocean ripples get stretched to macroscopic size
Credit: Sloan Digital Sky Survey
24
Geeng stronger 1.0
0.8
0.6
0.4
0.2
–3
–2
–1
1
2
3
25
Geeng stronger 1.0
0.8
0.6
0.4
0.2
Credit: NASA
–2
–1
1
2
3
distribu?on
–3
ΔT
25
Geeng stronger • If simple quantum
fluctuation, it must be distributed as Gaussian
1.0
0.8
0.6
0.4
0.2
Credit: NASA
–2
–1
1
2
3
distribu?on
–3
ΔT
25
Geeng stronger • If simple quantum
fluctuation, it must be distributed as Gaussian
1.0
0.8
0.6
0.4
0.2
–3
Credit: NASA
–2
–1
1
2
3
distribu?on
•
Indeed!
ΔT
25
Geeng stronger • If simple quantum
fluctuation, it must be distributed as Gaussian
1.0
0.8
0.6
• Indeed! • further tests of non-
0.4
0.2
Gaussianity at Planck
Credit: NASA
–2
–1
1
2
3
distribu?on
–3
ΔT
25
• •
infla?on
scalar field with rather flat potential (compared to the Planck scale), λ≈10–11 the equation of motion has a “friction term”
V(φ) φ
¨+ ¨ +3H ˙ =V V0 (0 () ) 3H˙ =
• slow-roll solution with more or less constant H
| ¨| ⌧ | ˙ | = V 0 ( ) H 2 =
8⇡ V 3 MP2 l
• Universe expands exponentially R(t) ∝ e • need e-folding N=Ht > 60 to
φ t
Ht
solve the problem
log R t
HM, Suzuki, Yanagida, Yokoyama
26
S?ll many mysteries • What caused inflation? • What time? • How much? • Definitive proof? 27
S?ll many mysteries • What caused inflation? • What time? • How much? • Definitive proof?
E-‐mode
B-‐mode polariza?on
27
How do we know it really happened?
• everything gets quantum
fluctuation, including gravitons Gravitons from quantum fluctuation gives B-mode polarization in CMB The size is directly proportional to the inflationary energy scale ⇒ e.g., Planck, POLARBEAR, LiteBIRD
E-‐mode
B-‐mode
• •
28
How do we know it really happened?
• everything gets quantum
fluctuation, including gravitons Gravitons from quantum fluctuation gives B-mode polarization in CMB The size is directly proportional to the inflationary energy scale ⇒ e.g., Planck, POLARBEAR, LiteBIRD
•
E-‐mode
B-‐mode Credit: KEK CMB Group / JAXA
•
LiteBIRD
28
LiteBIRD sensi?vity
Credit: KEK LiteBIRD Working Group / JAXA
29 13.
rs
yrs
ky
8B
380
sec nth illio
in 3m
1 tr Higgs
CMB
Credit: C. Amsler et al. (Par?cle Data Group), Physics LeIers B667, 1 (2008)
30
8B 13.
rs
yrs
ky
380
sec nth illio ??? ec? –34 s
in 3m
1 tr 10
inflation
Higgs
CMB
Credit: C. Amsler et al. (Par?cle Data Group), Physics LeIers B667, 1 (2008)
30
fate of the Universe
Credit: NASA
31
expansion
same as a ball
32
expansion
same as a ball
32
expansion
same as a ball
decelera?on
32
three possible fates • if large amount of matter,
expansion stops and heads back to a Big Crunch expansion will go on forever
• study the expansion
history and predict the future!
size of the Universe
• if small amount of matter,
?me
33
three possible fates • if large amount of matter,
expansion stops and heads back to a Big Crunch Credit: NASA
expansion will go on forever
• study the expansion
history and predict the future!
size of the Universe
• if small amount of matter,
?me
33
Future observers
34
Future observers • as the Universe gets
bigger, we will be able to see more and more galaxies
• the observation becomes more fun!
34
Dark Energy
Credit: NASA
35
Credit: NASA
36 Dark Energy
Dark Energy Dark Energy
Dark Energy Dark Energy
Dark Energy Dark Energy
Dark Energy
Dark Energy
Dark Energy Dark Energy Credit: NASA
Dark Energy Dark Energy
Dark Energy Dark Energy
36
Type-‐Ia supernovae
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae • Type-Ia supernova
becomes brighter than the whole galaxy
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae • Type-Ia supernova •
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae • Type-Ia supernova • •
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time How red it looks ⇒ How much expansion
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae • Type-Ia supernova • • •
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time How red it looks ⇒ How much expansion Expansion of the Universe is getting faster!
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae Credit: KMJ, CC BY-‐SA 3.0
• Type-Ia supernova • • •
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time How red it looks ⇒ How much expansion Expansion of the Universe is getting faster!
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae Supernova Cosmology Project (Amanullah, et al., 2010)
Credit: KMJ, CC BY-‐SA 3.0
• Type-Ia supernova
•
n ?o era ?on l e acc celera de Supernova Cosmology Project (PerlmuIer, et al., 1998)
37 Supernova Cosmology Project Supernova Cosmology Project (Knop, et al., 2010)ΩΜ , ΩΛ Knop et al. (2003)
0.25,0.75 0.25, 0 1, 0
24
Supernova Cosmology Project
22
Credit: NASA Thermonuclear Supernovae (PerimuIer, et al., 1997)
effective mB
•
20
18
Calan/Tololo & CfA 16
14 1.0
supernovae on demand
mag. residual from empty cosmology
•
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time How red it looks ⇒ How much expansion Expansion of the Universe is getting faster!
ΩΜ , ΩΛ
0.5
0.25,0.75
0.0
0.25, 0
0.5 1.0 0.0
1,
0.2
0.4
0.6
0.8
0
1.0
redshift z
38
stretch factor • it is not quite standard • correlation between duration time and the absolute brightness
• can be “fixed” by a “stretch factor”
• other smaller concerns with environment (metallicity), dust extinction, etc
39 Pierre An?logus Marc Betoule Stat ~ x 10 since the 1998 discovery papers
14 HST SNe Ia (z~0.7-1.4), Riess 2007 242 SNLS SNe Ia (z~0.2-1), Sullivan 2011 93 SDSS SNe Ia (z~0.1-0.4), Holzman 2009 123 Low-z SNe Ia (z~0.05), Hamuy96, …. 472 SNe Ia total
Guy et al, 2010 – Conley et al 2010, Sullivan et al, 2011 Dark Energy - Blois 2012
9
40 expansion
41 expansion
41
expansion
same as a ball
expansion
same as a ball
size of the Universe
41
should slow down ?me
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr)
41
same as a ball
size of the Universe
expansion
speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing!
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong?
41
same as a ball
size of the Universe
expansion
speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong? • new paradigm of the Universe, fundamental laws
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong? • new paradigm of the Universe, fundamental laws • If the rate of energy increase very quick, eventually the expansion becomes infinitely fast ⇒ Will the Universe end??
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong? • new paradigm of the Universe, fundamental laws • If the rate of energy increase very quick, eventually the expansion becomes infinitely fast ⇒ Will the Universe end??
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong? • new paradigm of the Universe, fundamental laws • If the rate of energy increase very quick, •
eventually the expansion becomes infinitely fast ⇒ Will the Universe end?? Need to measure the rate of energy increase!
41
Accelera?on • w: equation of state parameter
• radiation: w=1/3 • matter: w=0 • vacuum energy: w=–1 • acceleration: w
1 Credit: NASA
How did the Universe begin? What is its fate? What is it made of? What are its fundamental laws? Where do we come from? Now in the realm of science!
Credit:(aNGeLic!(by(Rolfe(Kolbe( h7p://www.flickr.com/photos/46210293@N08/8287418426/(
2
Outline 1. From daily life to Big Bang 2. Birth of elements and Higgs boson 3. Dark matter and anti-matter 4. Inflation and Dark energy
3
4. Infla?on and Dark Energy
4
Infla?on
Credit: NASA
5
8B
13.
rs ky 380
yrs
in 3m ec th s lion -bil ten sec nth illio
1 tr
Higgs DM
CMB
Credit: C. Amsler et al. (Par?cle Data Group), Physics LeIers B667, 1 (2008)
6
yrs
rs ky
8B
13.
380
in 3m ec th s lion -bil ten sec nth illio 1 tr Higgs DM
CMB
Credit: C. Amsler et al. (Par?cle Data Group), Physics LeIers B667, 1 (2008)
6 A one million mark note used as a notepad
Credit: Bundesarchiv, Bild 183-‐R1215-‐506, CC BY-‐SA 3.0
Credit: Bundesarchiv, Bild 102-‐00193, CC BY-‐SA 3.0
Credit: Bundesarchiv, Bild 102-‐00104 / Pahl, Georg, CC BY-‐SA 3.0
Notes used as wallpaper
Hundred billion mark note
7
Credit: Dr Graham Beards, CC BY 3.0
Credit: NASA
8
Credit: Dr Graham Beards, CC BY 3.0
Credit: NASA
8
Credit: Dr Graham Beards, CC BY 3.0
>1026
Credit: NASA
8
Why do they all look the same?
• Like having discovered two
remote islands in very different parts of the world, speaking the same language
• even the accents are nearly the same: one part in 100,000
• we suspect they had Credit: NASA
communication
9
10
11 fly-‐by simula?on based on real data
Credit: Sloan Digital Sky Survey
12 fly-‐by simula?on based on real data
Credit: Sloan Digital Sky Survey
about ten trillion ?mes faster than light
12
fly-‐by simula?on based on real data
Credit: Sloan Digital Sky Survey
about ten trillion ?mes faster than light prac?cally the same no maIer how far you go
12
more or less uniform small winkles
2 billion light years
Credit: Sloan Digital Sky Survey
13
equa?on for cosmic expansion m
R M
14
equa?on for cosmic expansion m
R M
14
equa?on for cosmic expansion F = ma
m
R M
14
equa?on for cosmic expansion F = ma
F =
G
Mm R2
m
R M
14
equa?on for cosmic expansion F = ma
F = a=
G
Mm R2
d2 R dt2
m
R M
14
equa?on for cosmic expansion F = ma
F = a=
G
Mm R2
d2 R dt2
m
R M
2
M d R = −G 2 R dt 2
14
equa?on for cosmic expansion F = ma
F =
G
Mm R2
m
R
d2 R dt2
a=
M
2
M d R = −G 2 R dt 2 "=
1 2
✓
dR dt
◆2
G
M R
14
equa?on for cosmic expansion F = ma
F =
G
Mm R2
m
R
d2 R dt2
a=
M
2
M d R = −G 2 2 R dt conserved ✓ ◆2 "=
dR dt
1 2
G
M R
14
equa?on for cosmic expansion F = ma
F =
G
Mm R2
m
R
d2 R dt2
a=
M
2
M d −G 2 2R = R dt conserved ✓ ◆2 "=
1 2
dR dt
G
M =0±0.01 R
14
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M R =0
R M
15
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M =0 R
in terms of mass density ρ
R M
15
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M =0 R
in terms of mass density ρ M=
4⇡ 3 ⇢R 3
R M
15
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M =0 R
in terms of mass density ρ M=
R˙ R
!2
4⇡ 3 ⇢R 3
=
R M
8⇡ G⇢ 3
15
equa?on for cosmic expansion conserved ✓ ◆ "=
1 2
dR dt
2
G
M R =0
in terms of mass density ρ M=
R˙ R
!2
4⇡ 3 ⇢R 3
=
R M
8⇡ G⇢ 3
Friedmann equa?on
15
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
R M
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ
R M
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ 3
R M
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ =const 3
R M
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ =const 3
R M
dR = HR dt
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ =const 3
R M
dR = HR dt
R(t) = R(0) e Ht
16
equa?on for cosmic expansion
Friedmann equa?on R˙ R
!2
=
8⇡ G⇢ 3
if constant mass density ρ H2 =
8⇡ G⇢ =const 3
R M
dR = HR dt
R(t) = R(0) e Ht Universe expands exponen?ally!
16
17
constant energy per volume
1
17
constant energy per volume
1
8
17
constant energy per volume
1
8
total energy keeps growing like volume R(t)3∝e3Ht
17
constant energy per volume
1
8
total energy keeps growing like volume R(t)3∝e3Ht energy grows like volume makes the expansion faster energy grows even more
17
Ul?mate Free Lunch! constant energy per volume
1
8
total energy keeps growing like volume R(t)3∝e3Ht energy grows like volume makes the expansion faster energy grows even more
17
Ul?mate Free Lunch! constant energy per volume
1
8
total energy keeps growing like volume R(t)3∝e3Ht energy grows like!!volume makes the expansion faster energy grows even more
17
catch: Uncertainty Principle
18
physics is uncertain
Credit: © Hitachi, Ltd. 1994, 2013. All rights reserved.
Akira Tonomura
19
physics is uncertain
Credit: © Hitachi, Ltd. 1994, 2013. All rights reserved.
Akira Tonomura
19
interference of waves
a par?cle is a wave a wave is a par?cle
20
interference of waves
a par?cle is a wave a wave is a par?cle
20
quantum mechanics • law of physics at subatomic scales • uncertainty principle • you can’t predict what happens each time • but over time you find a regular pattern • a particle is a wave • a wave is a particle • when squeezed into narrow
Credit: Armedblowfish, BSD
space, wave is amplified
21
quantum mechanics • law of physics at subatomic scales • uncertainty principle • you can’t predict what happens each time • but over time you find a regular pattern • a particle is a wave • a wave is a particle • when squeezed into narrow
Credit: Armedblowfish, BSD
space, wave is amplified
21
quantum mechanics • law of physics at subatomic scales • uncertainty principle • you can’t predict what happens each time • but over time you find a regular pattern • a particle is a wave • a wave is a particle • when squeezed into narrow
Credit: Armedblowfish, BSD
space, wave is amplified
21
near sighted • What you are seeing one
moment is gone by inflation the next moment
• feel very near-sighted • “horizon” ≈ H • small space I
–1
⇒big uncertainty
22
near sighted • What you are seeing one
moment is gone by inflation the next moment
• feel very near-sighted • “horizon” ≈ H • small space I
–1
⇒big uncertainty
22
near sighted • What you are seeing one
moment is gone by inflation the next moment
• feel very near-sighted • “horizon” ≈ H • small space I
–1
⇒big uncertainty
22
vacuum is ac?ve
Quantum Chromodynamics movies are provided at hNp://www.physics.adelaide.edu.au/theory/ staff/leinweber/VisualQCD/Nobel/
23
seed for diversity • universe was born tiny • entire visible universe was • • •
smaller than 10–26 cm ripples were made by uncertain principle only 1mm ripple on 100m deep ocean ripples get stretched to macroscopic size
24
seed for diversity • universe was born tiny • entire visible universe was • • •
Credit: NASA
smaller than 10–26 cm ripples were made by uncertain principle only 1mm ripple on 100m deep ocean ripples get stretched to macroscopic size
Credit: Sloan Digital Sky Survey
24
Geeng stronger 1.0
0.8
0.6
0.4
0.2
–3
–2
–1
1
2
3
25
Geeng stronger 1.0
0.8
0.6
0.4
0.2
Credit: NASA
–2
–1
1
2
3
distribu?on
–3
ΔT
25
Geeng stronger • If simple quantum
fluctuation, it must be distributed as Gaussian
1.0
0.8
0.6
0.4
0.2
Credit: NASA
–2
–1
1
2
3
distribu?on
–3
ΔT
25
Geeng stronger • If simple quantum
fluctuation, it must be distributed as Gaussian
1.0
0.8
0.6
0.4
0.2
–3
Credit: NASA
–2
–1
1
2
3
distribu?on
•
Indeed!
ΔT
25
Geeng stronger • If simple quantum
fluctuation, it must be distributed as Gaussian
1.0
0.8
0.6
• Indeed! • further tests of non-
0.4
0.2
Gaussianity at Planck
Credit: NASA
–2
–1
1
2
3
distribu?on
–3
ΔT
25
• •
infla?on
scalar field with rather flat potential (compared to the Planck scale), λ≈10–11 the equation of motion has a “friction term”
V(φ) φ
¨+ ¨ +3H ˙ =V V0 (0 () ) 3H˙ =
• slow-roll solution with more or less constant H
| ¨| ⌧ | ˙ | = V 0 ( ) H 2 =
8⇡ V 3 MP2 l
• Universe expands exponentially R(t) ∝ e • need e-folding N=Ht > 60 to
φ t
Ht
solve the problem
log R t
HM, Suzuki, Yanagida, Yokoyama
26
S?ll many mysteries • What caused inflation? • What time? • How much? • Definitive proof? 27
S?ll many mysteries • What caused inflation? • What time? • How much? • Definitive proof?
E-‐mode
B-‐mode polariza?on
27
How do we know it really happened?
• everything gets quantum
fluctuation, including gravitons Gravitons from quantum fluctuation gives B-mode polarization in CMB The size is directly proportional to the inflationary energy scale ⇒ e.g., Planck, POLARBEAR, LiteBIRD
E-‐mode
B-‐mode
• •
28
How do we know it really happened?
• everything gets quantum
fluctuation, including gravitons Gravitons from quantum fluctuation gives B-mode polarization in CMB The size is directly proportional to the inflationary energy scale ⇒ e.g., Planck, POLARBEAR, LiteBIRD
•
E-‐mode
B-‐mode Credit: KEK CMB Group / JAXA
•
LiteBIRD
28
LiteBIRD sensi?vity
Credit: KEK LiteBIRD Working Group / JAXA
29 13.
rs
yrs
ky
8B
380
sec nth illio
in 3m
1 tr Higgs
CMB
Credit: C. Amsler et al. (Par?cle Data Group), Physics LeIers B667, 1 (2008)
30
8B 13.
rs
yrs
ky
380
sec nth illio ??? ec? –34 s
in 3m
1 tr 10
inflation
Higgs
CMB
Credit: C. Amsler et al. (Par?cle Data Group), Physics LeIers B667, 1 (2008)
30
fate of the Universe
Credit: NASA
31
expansion
same as a ball
32
expansion
same as a ball
32
expansion
same as a ball
decelera?on
32
three possible fates • if large amount of matter,
expansion stops and heads back to a Big Crunch expansion will go on forever
• study the expansion
history and predict the future!
size of the Universe
• if small amount of matter,
?me
33
three possible fates • if large amount of matter,
expansion stops and heads back to a Big Crunch Credit: NASA
expansion will go on forever
• study the expansion
history and predict the future!
size of the Universe
• if small amount of matter,
?me
33
Future observers
34
Future observers • as the Universe gets
bigger, we will be able to see more and more galaxies
• the observation becomes more fun!
34
Dark Energy
Credit: NASA
35
Credit: NASA
36 Dark Energy
Dark Energy Dark Energy
Dark Energy Dark Energy
Dark Energy Dark Energy
Dark Energy
Dark Energy
Dark Energy Dark Energy Credit: NASA
Dark Energy Dark Energy
Dark Energy Dark Energy
36
Type-‐Ia supernovae
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae • Type-Ia supernova
becomes brighter than the whole galaxy
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae • Type-Ia supernova •
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae • Type-Ia supernova • •
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time How red it looks ⇒ How much expansion
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae • Type-Ia supernova • • •
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time How red it looks ⇒ How much expansion Expansion of the Universe is getting faster!
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae Credit: KMJ, CC BY-‐SA 3.0
• Type-Ia supernova • • •
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time How red it looks ⇒ How much expansion Expansion of the Universe is getting faster!
Supernova Cosmology Project (PerlmuIer, et al., 1998)
37
Type-‐Ia supernovae Supernova Cosmology Project (Amanullah, et al., 2010)
Credit: KMJ, CC BY-‐SA 3.0
• Type-Ia supernova
•
n ?o era ?on l e acc celera de Supernova Cosmology Project (PerlmuIer, et al., 1998)
37 Supernova Cosmology Project Supernova Cosmology Project (Knop, et al., 2010)ΩΜ , ΩΛ Knop et al. (2003)
0.25,0.75 0.25, 0 1, 0
24
Supernova Cosmology Project
22
Credit: NASA Thermonuclear Supernovae (PerimuIer, et al., 1997)
effective mB
•
20
18
Calan/Tololo & CfA 16
14 1.0
supernovae on demand
mag. residual from empty cosmology
•
becomes brighter than the whole galaxy How bright it looks ⇒ How far away ⇒ How far back in time How red it looks ⇒ How much expansion Expansion of the Universe is getting faster!
ΩΜ , ΩΛ
0.5
0.25,0.75
0.0
0.25, 0
0.5 1.0 0.0
1,
0.2
0.4
0.6
0.8
0
1.0
redshift z
38
stretch factor • it is not quite standard • correlation between duration time and the absolute brightness
• can be “fixed” by a “stretch factor”
• other smaller concerns with environment (metallicity), dust extinction, etc
39 Pierre An?logus Marc Betoule Stat ~ x 10 since the 1998 discovery papers
14 HST SNe Ia (z~0.7-1.4), Riess 2007 242 SNLS SNe Ia (z~0.2-1), Sullivan 2011 93 SDSS SNe Ia (z~0.1-0.4), Holzman 2009 123 Low-z SNe Ia (z~0.05), Hamuy96, …. 472 SNe Ia total
Guy et al, 2010 – Conley et al 2010, Sullivan et al, 2011 Dark Energy - Blois 2012
9
40 expansion
41 expansion
41
expansion
same as a ball
expansion
same as a ball
size of the Universe
41
should slow down ?me
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr)
41
same as a ball
size of the Universe
expansion
speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing!
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong?
41
same as a ball
size of the Universe
expansion
speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong? • new paradigm of the Universe, fundamental laws
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong? • new paradigm of the Universe, fundamental laws • If the rate of energy increase very quick, eventually the expansion becomes infinitely fast ⇒ Will the Universe end??
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong? • new paradigm of the Universe, fundamental laws • If the rate of energy increase very quick, eventually the expansion becomes infinitely fast ⇒ Will the Universe end??
expansion
same as a ball
size of the Universe
41 speeding up! should slow down ?me
• expansion started to speed up recently (~7Byr) • energy is increasing! • infinite source of energy?? dark energy • Was Einstein wrong? • new paradigm of the Universe, fundamental laws • If the rate of energy increase very quick, •
eventually the expansion becomes infinitely fast ⇒ Will the Universe end?? Need to measure the rate of energy increase!
41
Accelera?on • w: equation of state parameter
• radiation: w=1/3 • matter: w=0 • vacuum energy: w=–1 • acceleration: w
