Random (biased) thoughts on Inflation 2

A01 brainstorming meeting

Kavli IPMU

6-7 December, 2018

1

Misao Sasaki

C01 究極理論

A02 大規模構造理論

佐々木節 trans-Planckian phys

Open inflation

高橋智＊ scale dependence non-Gaussianity

山口昌英＊ quantum GWs 2nd order GWs

横山順一＊ SUSY inflation

primordial mag fields

須山輝明 small scale fluct’ns non-linear effects

中山和則 particle physics models

reheating

横山修一郎isocurvature fluct’ns mode-mode coupling

B01 CMB観測 A03 ダークエネルギー A01インフレーション

B02+03 宇宙論的構造観測

D01 データ解析

小林努 scalar-tensor theory

modified gravity

inflaton model string landscape/ multiverse

NL evolution numerical sim’s

＊分担者

A01班構成 2

Inflation Current Status

3

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

4

Reheating stage

(102~107(?)cm)

Planck constraints on inflation

scalar spectral index: ns ~ 0.96

tensor-to-scalar ratio: r < 0.1 (95%CL)

simplest model excluded

( )

( )

T

S

P kr

P k

3log[ ( )]1

log

Ss

d k P kn

d k

2V

Planck 2015 (2018)XX

2V

5

• 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

(m22 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 6

Beyond (standard model of)

Inflation

7

• 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 R ( ) 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?

8

• “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 9

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

10

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/2p

expansion rate

11

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 12

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), …

13

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

14

supercurvature (SC) mode? 15

• if the amplitude of SC mode is large, could it mimic a closed universe?

32 8

6 3

( )

( ) ((

))R x G

H x xp

r

• separate universe (lowest order gradient expansion)

3 3

2

1

6 6

( ) ( )( ) ( )R x R x

a

3

2

2

6

2 4

3

( )( )( )SCpR xx

a

2

30 4

2 4SC mode may dominate if | ( )| ~ .~

( )

SC xp

2 3 21 0 1 0discrete mode with ( ): ( ) ( )p p Y x

2 23 4 10fluctuation i |f ~ ( )| ~SC xs

• Observational signatures/tests?

22 2 2 2

2possi with ble inf

inf

SC FVBD FV

HO H H

H

MS & Tanaka, 1996

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? 16

PBHs and GWs at 2nd order perturbation

17

Saito & Yokoyama,arXiv:0912.5317

(ΩPBHℎ2, 𝑀PBH) = (10−5, 100𝑀⊙)

𝒫𝐺𝑊(𝑘) ∼ 𝒫𝑆(𝑘)2

(ΩPBHℎ2, 𝑀PBH) = (10−1,1020 g)

𝒫𝑆(𝑘) ≳ 10−2.5 for PBH formation

≳ 10−5 >>10-10

18

Non-Gaussianity Effect?

ℛ(𝑥) = ℛ𝑔(𝑥)

RG Cai, S Pi & MS, arXiv:1810.11000

PBH constraints:

If PBHs=CDM LISA must detect

induced GWs!

𝑀PBH = 1022g

+𝐹NL ℛ𝑔2(𝑥) − ⟨ℛ𝑔

2(𝑥)⟩

Future (current?) issues

19

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

20

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?

21

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?

22

• initial condition for inflation, multiverse?

• successful reheating?

• non-linear effects, non-zero field space curvature?

• inflationary models for PBHs? non-Gaussianities?

• massive gravity?

• swampland?……

• 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

Domenech & MS ‘15

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