Misao Sasaki
KIAS-YITP joint workshop 22 September, 2017
Introduction
2
Inflation: the origin of Big Bang
Inflation is a quasi-exponential expansion of the Universe at its very early stage; perhaps at t~10-36 sec.
It was meant to solve the initial condition (singularity, horizon &
flatness, etc.) problems in Big-Bang Cosmology: if any of them can be said to be solved depends on precise
definitions of the problems.
Quantum vacuum fluctuations during inflation turn out to play the most important role. They give the initial condition for all the structures in the Universe.
Cosmic gravitational wave background is also generated.
Brout, Englert & Gunzig ’77, Starobinsky ’79, Guth ’81, Sato ’81, Linde ’82,…
3
4
2 2 2 2
3
1
( )( ) ;
( ) sinh
ds dt a t dH
a t H Ht
温故知新 (learning from the past)
Creation of Open Universe!
Now in the context of String Landscape
log L
log a(t)
L=H-1
Size of the Observable Universe
Inflationary Universe Hot Bigbang Universe
length scales of the inflationary universe
L=H0-1
1028cm
108cm LIGO band
~ 46 e-folds
targets for multi-frequency GW astronomy
5
Reheating stage
(102~107(?)cm)
Dynamics
6
Zero-point (vacuum) fluctuations of f :
222
20 3 ;
() ( )
)(k k k
kt
tH t
af f f
( ) ik x
kk
t ef f
harmonic oscillator with friction term and time-dependent
kf const.
··· frozen when < H
(on superhorizon scales) fk
tensor (gravitational wave) modes also satisfy the same eq.
Starobinsky ‘79
Mukhanov ’81, ….
Seed of cosmological perturbations 7
Generation of Curvature Perturbation
curvature (potential) perturbation R :
t
xi
0
0f
0
0f
• f is frozen on “flat” (R=0) 3-surface (t=const. hypersurface)
• Inflation ends/damped osc starts “comoving” (f =const.) on 3-surface.
end of inflation
hot bigbang universe
const., 0cT
3 2
2
4( )Ra
0ff f
fc
H
ff
comoving curvature perturbation Rc ~ - Newton potential
8
• Spatially flat universe
• Almost scale invariant, adiabatic, Gaussian
primordial scalar (curvature) perturbations
• Almost scale invariant, Gaussian primordial tensor (gravitational wave) perturbations
Generates CMB anisotropy Origin of galaxies, stars, …
Generic predictions of inflation 9
• Amplitude of curvature perturbation:
• Power spectrum index: 1812 4 10 GeV: Planck mass
8~ .plM
G
Mukhanov (1985), MS (1986)
• Tensor (gravitational wave) spectrum:
Liddle-Lyth (1992)
2
2f
/
c
k a H
H
3
3
4
1
8 8
2
( )
(;
( )( )
)T S
T
T
n
T
kP k Ak
P k rn
P k
Quantitative Predictions
23 2
12
2
231 2
4
23
2
f
/
( ) ;( )
Sn
S
k a H
S P
k HP k Ak
V Vn M
V V
“consistency relation”
Stewart-Lyth (1993)
10
Observational results
11
Planck TT, TE & EE spectrum 12
2
2f
/
c
k a H
H
• Amplitude of curvature perturbation:
• Power spectrum index: 2
3 21
22
231 2
4
23
2
f
/
( ) ;( )
Sn
S
k a H
S P
k HP k Ak
V Vn M
V V
1812 4 10 GeV: Planck mass
8PM
G ~ .
Mukhanov (1985), MS (1986)
• Tensor (gravitational wave) spectrum: 3
3
4
1
8 8
2
( )
(;
( )( )
)T S
T
T
n
T
kP k Ak
P k rn
P k Liddle-Lyth (1992)
15
obs
4 16 10 Ge10 V?/
, )~ ( ~c V f
to be observed ...
Stewart-Lyth (1993)
Planck1 0 0355 1 0 04 0 0 049, ~ .. . SSn n for a typical model
Mukhanov & Chibisov (1981)
13
Planck constraints on inflation
scalar spectral index: ns ~ 0.96
tensor-to-scalar ratio: r < 0.1
simplest model is almost excluded
( )
( )
T
S
P kr
P k
3log[ ( )]1
log
Ss
d k P kn
d k
2V f
Planck 2015 XX
2V f
14
Implications
15
Inflation as the Origin of All Structures
of the Universe
16
• scalar spectral index: ns<1 at ~ 5 s
• tensor/scalar ratio: r < 0.1 implies Einflation < 1016 GeV
• simple, canonical models are on verge of extinction
(m2f2 model excluded at > 2 s)
• R2 (Starobinsky) model seems to fit best. But why?
(large R2 correction but negligible higher order terms)
• fNLlocal <O(1) suggests (effectively) single-field slow-roll
(but non-slow-roll models with fNLlocal =O(1) not excluded)
element of non-canonicality is needed
Current status 17
Beyond (standard model of)
Inflation
18
• Non-canonical kinetic term? (cs <1?)
• non-minimal coupling to gravity?
• scalar-tensor with derivative couplings (Hordeski) ?
2
1 1NL ( : sound speed) , equil
s
s s
P c fc c
Planck: cs > 0.024 at 95% CL
2V Rf f( ) 1TP kr
P k
( )
( ) Planck: > O(10)?
11 , ,, ,s s s Ts Tc cc c
tensor propagation speed
non-existence of
Einstein frame?
non-canonical models
• multi-field models, non-attractor inflation, … definition of
inflation?
19
• “Wiggles (dip)” in the power spectrum
• Suppressed large scale fluctuations
signature of a heavy field? Chen ’11, …
step/feature in potential? Leach et al. ’01, ….
non-BD vaccum? Easther et al. ’02,….
featured potential? open inflation? Linde, MS & Tanaka ’99, ….
Anomalies & Features 20
string theory suggests an intriguing picture of the early universe
Maybe we live in one of these vacua…
Cosmic Landscape?
taken from http://ineedfire.deviantart.com/art/Psychedelic-Multiverse-104313536
21
Universe jumps around in the landscape by quantum
tunneling
• it can go up to a vacuum with larger rv
• if it tunnels to a vacuum with negative rv ,
it collapses within t ~ MP/|rv|1/2.
• so we may focus on vacua with positive rv: dS vacua
0
rv
Sato, Kodama, MS & Maeda (’81)
de Sitter (dS) space ~ thermal state with T =H/2
expansion rate
22
Universe inside nucleated bubble = spatially open universe
Observational data indicate 1-W0 = WK,0 ~< 10-2 : almost flat
2
2
2 2
1
3 P
aH
a M a
r
Friedmann eq.
K2 2 2 2
11
3 PM H a H
r W W
negative spatial
curvature
density parameter
(“0” stands for current value)
Open Inflation in Cosmic Landscape 23
What if this is the case?
two possibilities
1. inflation after tunneling was short enough (N~60)
2 3
,0 01 10 ~10K
W W
,0 01 1KW W
2. inflation after tunneling was long enough (N>>60)
signatures from bubble collisions
“open universe”
“flat universe”
signatures in large angle CMB anisotropies?
Kanno, MS & Tanaka (‘13), White, Zhang & MS (’14), …
Sugimura, Yamauchi & MS (‘12), …
24
scalar suppression on large scales Linde, MS & Tanaka (1999)
White, Zhang & MS (2014)
scalar
tensor
(no suppression)
curvature
radius H0
-1 if WK ≈ 0.01
scalar suppression begins at smaller scale
break scale
25
dipole power asymmetry
dipole asymmetry in the direction
maximizing the asymmetry
no asymmetry in the direction of ell=1
1 2 ˆ( ; ) ( )isoP k A P k n d n
dipole line of sight
26
isoT
TA
T
T
cos1
Planck 2013 XXIII
0.07A
27
curvature radius
size of observable universe
Gradient of a field over the horizon scale = Super-curvature mode in open inflation
may modulate the amplitude of
perturbation depending on the direction.
leading order effect is dipolar
if this is the case, then
Kanno, MS & Tanaka ‘13 Brynes, Domenech, MS & Takahashi ‘16
MS, Tanaka & Yamamoto ‘95
310~K
W
28
Planck XVII • Slightly above 1-s
deviation from zero
• What if this is primordial?
may be due to TSS coupling in a massive tensor theory Domenech, Hiramatsu, Lin, MS, Shiraishi, Wang ‘16
500 2000
Scale-dependent non-Gaussianity? 29
Future issues
30
cosmological scales
# e-folds (~ 1/T)
Lcom
H0-1=10 Gpc
102 Mpc
108 cm
10-4 eV 1 eV 109 GeV 1015 GeV
102 cm
M
1024
1018
1015 g
M
M
L
model dep
inflation damped osc (matter-dom)
rad-dom matter-dom dark energy
Hinf-1
1015 GeV
(assuming Treheat>109GeV)
N ~ 50-60
beyond inflation?
very large scales
31
cosmological scales
# e-folds (~ 1/T)
Lcom
H0-1=10 Gpc
102 Mpc
108 cm
10-4 eV 1 eV 109 GeV 1015 GeV
102 cm
M
1024
1018
106
1015 g
M
M
M
L
model dep
inflation damped osc (matter-dom)
rad-dom matter-dom dark energy
Hinf-1
1015 GeV
(assuming Treheat>109GeV)
102 pc
intermediate scales
1 MeV
N ~ 35-50
behind inflation?
32
1 GeV
cosmological scales
# e-folds (~ 1/T)
Lcom
H0-1=10 Gpc
102 Mpc
0.1 pc
108 cm
10-4 eV 1 eV 109 GeV 1015 GeV
102 cm
M
1024
1018
106
1
1015 g
M
M
M
M
L
inflation damped osc (matter-dom)
rad-dom matter-dom dark energy
Hinf-1
1015 GeV
(assuming Treheat>109GeV)
102 pc
1 MeV
small scales
model dep
N ~ 10-30 particle physics?
33
• initial condition before inflation, multiverse?
• successful reheating?
• non-linear effects, non-Gaussianities?
• gravitational waves at second order, PBHs?
• massive gravity?
• ……
• definition of inflation? (conformal trans can give any expansion law)
2 2 2
2 2 2 2( )
( )( ) ( ) ( ) ( ),ds t ds
ds dt a t dx
dt t dt a t t a t
W W W
Identification of Inflaton!
Domenech & MS ‘15
34
Observational Inflationary Cosmology!
Inflation as the tool to explore physics of the early Universe
Era of
35
Appendix: recollections
• 2005 KIAS Cosmological Landscape: Strings, Gravity, and Inflation Organizers: Leonard Susskind (Stanford Univ.& KIAS) Kimyeong Lee (KIAS, Seoul) Piljin Yi (KIAS, Seoul) Misao Sasaki (YITP, Kyoto) Shigeki Sugimoto (YITP, Kyoto) • 2007 YITP String Phenomenology and Cosmology • 2009 KIAS Extended Workshop on DM, LHC and Cosmology • 2011 KIAS String Theory, Holography, and Beyond • 2013 YITP String Theory, Black Holes and Holography • 2015 KIAS Geometry in Gauge Theories and String Theory • 2017 YITP Strings, Gravity and Cosmology Organizers: Kimyeong Lee (KIAS) Sungjay Lee (KIAS) Shinji Mukhoyama (YITP) Misao Sasaki (YITP) Shigeki Sugimoto (YITP, Chair) Tadashi Takayanagi (YITP) Piljin Yi (KIAS)
May 2004 : MOU between KIAS and YITP (renewed in March 2008)
Appendix: recollections
• 2005 KIAS Cosmological Landscape: Strings, Gravity, and Inflation Organizers: Leonard Susskind (Stanford Univ.& KIAS) Kimyeong Lee (KIAS, Seoul) Piljin Yi (KIAS, Seoul) Misao Sasaki (YITP, Kyoto) Shigeki Sugimoto (YITP, Kyoto) • 2007 YITP String Phenomenology and Cosmology • 2009 KIAS Extended Workshop on DM, LHC and Cosmology • 2011 KIAS String Theory, Holography, and Beyond • 2013 YITP String Theory, Black Holes and Holography • 2015 KIAS Geometry in Gauge Theories and String Theory • 2017 YITP Strings, Gravity and Cosmology Organizers: Kimyeong Lee (KIAS) Sungjay Lee (KIAS) Shinji Mukhoyama (YITP) Misao Sasaki (YITP) Shigeki Sugimoto (YITP, Chair) Tadashi Takayanagi (YITP) Piljin Yi (KIAS)
May 2004 : MOU between KIAS and YITP (renewed in March 2008)
Appendix: recollections
• 2005 KIAS Cosmological Landscape: Strings, Gravity, and Inflation Organizers: Leonard Susskind (Stanford Univ.& KIAS) Kimyeong Lee (KIAS, Seoul) Piljin Yi (KIAS, Seoul) Misao Sasaki (YITP, Kyoto) Shigeki Sugimoto (YITP, Kyoto) • 2007 YITP String Phenomenology and Cosmology • 2009 KIAS Extended Workshop on DM, LHC and Cosmology • 2011 KIAS String Theory, Holography, and Beyond • 2013 YITP String Theory, Black Holes and Holography • 2015 KIAS Geometry in Gauge Theories and String Theory • 2017 YITP Strings, Gravity and Cosmology Organizers: Kimyeong Lee (KIAS) Sungjay Lee (KIAS) Shinji Mukhoyama (YITP) Misao Sasaki (YITP) Shigeki Sugimoto (YITP, Chair) Tadashi Takayanagi (YITP) Piljin Yi (KIAS)
May 2004 : MOU between KIAS and YITP (renewed in March 2008)
Appendix: recollections
• 2005 KIAS Cosmological Landscape: Strings, Gravity, and Inflation Organizers: Leonard Susskind (Stanford Univ.& KIAS) Kimyeong Lee (KIAS, Seoul) Piljin Yi (KIAS, Seoul) Misao Sasaki (YITP, Kyoto) Shigeki Sugimoto (YITP, Kyoto) • 2007 YITP String Phenomenology and Cosmology • 2009 KIAS Extended Workshop on DM, LHC and Cosmology • 2011 KIAS String Theory, Holography, and Beyond • 2013 YITP String Theory, Black Holes and Holography • 2015 KIAS Geometry in Gauge Theories and String Theory • 2017 YITP Strings, Gravity and Cosmology Organizers: Kimyeong Lee (KIAS) Sungjay Lee (KIAS) Shinji Mukhoyama (YITP) Misao Sasaki (YITP) Shigeki Sugimoto (YITP, Chair) Tadashi Takayanagi (YITP) Piljin Yi (KIAS)
May 2004 : MOU between KIAS and YITP (renewed in March 2008)
Appendix: recollections
• 2005 KIAS Cosmological Landscape: Strings, Gravity, and Inflation Organizers: Leonard Susskind (Stanford Univ.& KIAS) Kimyeong Lee (KIAS, Seoul) Piljin Yi (KIAS, Seoul) Misao Sasaki (YITP, Kyoto) Shigeki Sugimoto (YITP, Kyoto) • 2007 YITP String Phenomenology and Cosmology • 2009 KIAS Extended Workshop on DM, LHC and Cosmology • 2011 KIAS String Theory, Holography, and Beyond • 2013 YITP String Theory, Black Holes and Holography • 2015 KIAS Geometry in Gauge Theories and String Theory • 2017 YITP Strings, Gravity and Cosmology Organizers: Kimyeong Lee (KIAS) Sungjay Lee (KIAS) Shinji Mukhoyama (YITP) Misao Sasaki (YITP) Shigeki Sugimoto (YITP, Chair) Tadashi Takayanagi (YITP) Piljin Yi (KIAS)
May 2004 : MOU between KIAS and YITP (renewed in March 2008)
Appendix: recollections
• 2005 KIAS Cosmological Landscape: Strings, Gravity, and Inflation Organizers: Leonard Susskind (Stanford Univ.& KIAS) Kimyeong Lee (KIAS, Seoul) Piljin Yi (KIAS, Seoul) Misao Sasaki (YITP, Kyoto) Shigeki Sugimoto (YITP, Kyoto) • 2007 YITP String Phenomenology and Cosmology • 2009 KIAS Extended Workshop on DM, LHC and Cosmology • 2011 KIAS String Theory, Holography, and Beyond • 2013 YITP String Theory, Black Holes and Holography • 2015 KIAS Geometry in Gauge Theories and String Theory • 2017 YITP Strings, Gravity and Cosmology Organizers: Kimyeong Lee (KIAS) Sungjay Lee (KIAS) Shinji Mukhoyama (YITP) Misao Sasaki (YITP) Shigeki Sugimoto (YITP, Chair) Tadashi Takayanagi (YITP) Piljin Yi (KIAS)
May 2004 : MOU between KIAS and YITP (renewed in March 2008)
old physicists never die, they just fade away…
some say …
old physicists never die, they just fade away…
some say …
Thank You!
but I will NOT disappear yet!