Misao Sasaki - 京都大学kias-yitp2017/Sasaki.pdfMisao Sasaki (YITP, Kyoto) Shigeki Sugimoto (YITP, Kyoto) • 2007 YITP String Phenomenology and Cosmology • 2009 KIAS Extended

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



Hinf-1

1015 GeV


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



Hinf-1

1015 GeV


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)
















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some say …

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Documents

Misao Sasaki - 京都大学kias-yitp2017/Sasaki.pdfMisao Sasaki (YITP, Kyoto) Shigeki Sugimoto (YITP, Kyoto) • 2007 YITP String Phenomenology and Cosmology • 2009 KIAS Extended