Kazunori Nakayama- Gravitational wave background as a probe of reheating temperature of the Universe

8/3/2019 Kazunori Nakayama- Gravitational wave background as a probe of reheating temperature of the Universe

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Gravitational wave backgroundas a probe of reheating temperatureof the Universe

Kazunori NakayamaInstitute for Cosmic Ray Research,

University of Tokyo

KN, S.Saito,Y.Suwa, J.Yokoyama, arXiv:0802.2452, arXiv:0804.1827

SUSY08 @ COEX Center, Seoul (17/06/2008)


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Introduction


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Why reheating temperature ?Particle physics point of view

Some particle physics model can be

favored, constrained or excluded ifTR is determined observationally.

SUSY Gravitino Problem

Baryogenesis Constraintson TR

Particle physics in the LHC era Cosmology

TR

LHC New physics (Supersymmetry) ?

(Non)Thermal leptogenesis

Affleck-Dine baryogenesis


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Thermal history of the Universe

InflationInflaton

oscillationRadiationdominate

Matterdominate

TR

Reh

eati

ng

log a

a3

a

a4


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InflationInflaton


Matterdominate

TR

Reh

eati

ng

log a

a3

a

a4

BBN begins atT ~ 1MeV

well understood


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InflationInflaton


Matterdominate

TR

Reh

eati

ng

log a

a3

a

a4

BBN begins atT ~ 1MeV

well understoodpoorly understood


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Photon


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Photon

Neutrin

o


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Photon

Neutrin

o

Howtoe

xplore

thisepoch

?


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G

ravitationalW

ave

Photon

Neutrin

o

Howtoe

xplore

thisepoch

?


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Inflationary

Gravitational WaveBackground


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Generation of Gravitational Waves

ds2 = a2(t)[d2 + (ij + 2hij)dx

idx

j ]

Metric perturbation (tensor part)

hij =1

MP

=+,

d3k

(2)3/2h

k(t)eikx

e

ij

Same as massless field

hkh

k =

H2

inf

2k33(k k)

Quantization

Dimensionlesspower spectrum

2

h(k) = 64GHinf

2

2

r =

2

h

2R

= 16

Tensor-to-scalar ratio :

during inflation


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Evolution of GW

Outside the horizon :

Inside the horizon :

h

k + 3Hh

k +k

a2h

k = 0

h

k= const.

k a

1

dgw

d ln k=

132G

k2|h

k|2ain(k)a0

2

k4

for k < keq

k2

for k > keq

gw(k) = 1c

dgw

d ln k k for k < keq const for k > keq

Thermal history is imprinted in the GWB spectrum

Seto, Yokoyama (03), Boyle, Steinhardt (05), Boyle, Buonanno (07)


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Effect of reheating

Generation

of GWBG


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Effect of reheating

Generation

of GWBG

Horizon entryduring MD era


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Effect of reheating

Generation

of GWBG


Horizon entryduring RD era


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Effect of reheating

Generation

of GWBG



Horizon entry

during

D era


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Effect of reheating

Generation

of GWBG



Horizon entry

during

D era

Extra suppression to GW

spectrum for this mode

f > fR = 0.026HzTR

106GeV


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R.D.M.D.

.D.

Horizon entryduring

Gravitational Wave Spectrum

DECIGO

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGO

correlated


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Normalizationis determined

by r

R.D.M.D.

.D.

Horizon entryduring


DECIGO

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGO

correlated


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by r

R.D.M.D.

.D.

Horizon entryduring


DECIGO

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGO

correlated

Bending point isdetermined by TR


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by r

R.D.M.D.

.D.

Horizon entryduring


DECIGO

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGO

correlated


CMBpolarization


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by r

R.D.M.D.

.D.

Horizon entryduring


DECIGO

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGO

correlated


CMBpolarization


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by r

R.D.M.D..D.

Horizon entryduring


DECIGO

DECIGOcorrelated

ultimate-DECIGO

ul-DECIGO

correlated


CMBpolarization Direct detection


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10!6

10!5

10!4

10!3

10!2

10!1

100

10!16

10!14

10!12

10!10

10!8

10!6

fr/ Hz

!gw

Extrapolated

Extragalactic

Average

Astrophysical foreground

White Dwarf binary

Farmer and Phinney (03)

Completely

stochastic

Cannot beremoved.

Merger of WDbinary

GravitationalWaves


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Future observationscan determineor constrain TR

DECIGO-correlated ultimate-DECIGO

ultimate-DECIGO (corr)

TR can be determined

GW can be detected


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Future observationscan determineor constrain TR



TR can be determined

GW can be detected


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Implications onParticle Physics


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Gravitino Problem

Gravitino lifetime CM2P

m33/2

1 sec for m3/2 10TeV

Affect BBN

Unstable gravitino

Stable gravitino Overclosure bound

Thermal Production

Y3/2 2 1012

1 +m

2

g

3m23/2

TR

1010GeV

.

Khlopov, Linde (84), Ellis, Kim, Nanopoulos (84),Moroi, Murayama, Yamaguchi (93),

Bolz, Brandenburg, Buchmuller (01),Kawasaki, Kohri, Moroi (05), Pradler, Steffen (07)

Upper bound on TR

From scattering of particles in thermal bath

Photo-dissociationHadro-dissociation

p-n conversion

TR


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Stable Gravitino

Inflaton decay = 1015GeVm = 10

13GeV

Kawasaki,Takahashi,Yanagida(07)Endo,Takahashi,Yanagida(07)


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Stable GravitinoMay be determinedfrom accelerator

experiments


13GeV



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experiments

Accesible withfuture GW

experiment


13GeV



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experiments

Accesible withfuture GW

experiment

Check of the gravitino

dark metter scenario


13GeV



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LHC coming soon

Neutralino LSP

Gravitino LSP

Suppose that LHC will find SUSY anddetermine what is the LSP.

Direct detection

Indirect detectionNeutralino-nucleon scattering

Gamma-ray, positron, Neutrino,...

Next : In order to confirm LSP is dark matter...

Gravitational wavebackground detection

Reheating temperature of the universe


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Summary

Gravitational wave background provides a way todetermine reheating temperature of the Universe.

DECIGO/BBO can determine/constrain TR

CMB Polarization : r 10

Together with accelerator experiments,some particle physics (SUSY) models will be

favored/constrained.

TR 107GeV / TR 10

7GeV


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Back-up Slides


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Late-timeEntropy Production

L d


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Inflaton

Moduli

log a

TT

Late-time entropy productionStandard thermal history of the Universe may not hold.

Heavy Modulicompactification of extra D in string theory m m3/2

1

4

m3

M2P

T 170 MeV m

103 TeV

3/2

Decay of moduli produceshuge entropy

Large initial amplitude

dominate the Universe

L d


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Inflaton

Moduli

log a

TT

Dilution ofbaryon asymmetry

Kawasaki ,KN (07)

AD mechanism



1

4

m3

M2P

T 170 MeV m

103 TeV

3/2



dominate the Universe

L d


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Inflaton

Moduli

log a

TT


Kawasaki ,KN (07)

AD mechanism



1

4

m3

M2P

T 170 MeV m

103 TeV

3/2



dominate the UniverseNonthermal

dark matter frommoduli decay

Moroi,Randall(00), Nagai,KN (07)

L i d i


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Inflaton

Moduli

log a

TT


Kawasaki ,KN (07)

AD mechanism



1

4

m3

M2P

T 170 MeV m

103 TeV

3/2



dominate the UniverseNonthermal

dark matter frommoduli decay

Moroi,Randall(00), Nagai,KN (07)

Gravitino

overproduction frommoduli decay

Endo,Hamaguchi,Takahashi (06)Nakamura, Yamaguchi (06)


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0

20

40

60

0

20

40

60

0

20

40

60

0

20

40

60

0

20

40

60

Polonyi Singlet scalar to break SUSY

Q-ball Nontopological soliton formed

through Affleck-Dine mechanism

TQ 10GeV

1022

Q

1/2

T 170 MeV m

103 TeV3/2

Once Q-ball is formed, decay rateof the AD field is determinedby the surface area of Q-ball

Planck-suppressed interaction

Q: Baryon number of Qball

Moroi,Yamaguchi,Yanagida(96),Kawasaki,Moroi,Yanagida(96)

Fujii,Hamaguchi(02), Kawasaki, KN(07)

Kasuya, Kawasaki(00)

Kusenko (97)


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Saxion

Scalar partner of the axion in SUSY axion model

Interaction is suppressed by PQ scalefPQ 101012GeV

T 1GeV ms

1 TeV

3/21011 GeVfPQ

Note: s 2a

must be suppressed

M.Kawasaki, KN(08)

(s 2a) =f2

64

m3s

f2PQ

Ba =(s 2a)

total 0.2

Rajagopal,Turner,Wilczek(91),Chun,Lukas(95)Asaka,Yamaguchi(98),Kawasaki,KN,Senami(08)


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F =s(T)a

3(T)

s(TR)a3(TR)Dilution factor

F =TR

T

2

i

3M2P

=

Tosc

TRif Tosc < TR

= 1 else

initial amplitude i

oscillation begins at = m (T = Tosc)decay temperature

Dilute dangerous relics such as gravitinoproduced during reheating stage

Y3/2 Y3

/2/F

: late-decaying scalar


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Generation

of GWBG


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Generation

of GWBG

Additional matter dominated phasemodifies GW spectrum

G it ti l W S t


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r=0.1

G it ti l W S t


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TR


r=0.1

G it ti l W S t


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TR

T


r=0.1

G it ti l W S t


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Suppression

is determinedby F

TR

T


r=0.1



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Suppression

is determinedby F

TR

T


Thermal history is imprinted in GW spectrum

r=0.1


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Future observationsare also sensitive to

non-standardcosmology

F, TR can be determined

GW can be detected

U t bl iti


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Unstable gravitino

Kawasaki,Kohri,Moroi(05)

U t bl iti


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Consistency check ofgravitino mass/SUSY model

Unstable gravitino


U t bl iti


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Consistency check ofgravitino mass/SUSY model

Thermal leptogenesismay be excluded

Unstable gravitino


SUSY axion model Kawasaki KN Senami(08)


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8

-2

0

2

4

6

-4

8

-2

0

2

4

6

-4

logTR[GeV]

keV TeVGeVMeV GeVMeVkeVTeV

ms

Axino

GravitinoN_nu

CMB

BBN

reinonization

diffuse X

matter density LSP

(a) (b)

(c) (d)

s 2af=1: f=0:main 2a forbidden

KSVZ f=1 KSVZ f=0

DFSZ f=1 DFSZ f=0

Fa = 1012

GeV

Kawasaki,KN,Senami(08)

SUSY axion model

Kawasaki KN Senami(08)


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8

-2

0

2

4

6

-4

8

-2

02

4

6

-4

logTR[GeV]

keV TeVGeVMeV GeVMeVkeVTeV

ms

Axino

GravitinoN_nu

CMB

BBN

reinonization

diffuse X

matter density LSP

(a) (b)

(c) (d)

s 2af=1: f=0:main 2a forbidden

KSVZ f=1 KSVZ f=0

DFSZ f=1 DFSZ f=0

Fa = 1012

GeV

GW detection may

have implications onSUSY axion model

Kawasaki,KN,Senami(08)


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SUSY inflation

SUSY Stable against radiative correction

Flat potential

However, in supergravity

problem


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For minimal Kahler

V = exp

K

M2P

K

ijDiW(DjW) 3

|W|2

M2P

.

K=

VVinf

M2P

||2 O(1)

This term cancels if W has the form

W= f()

For non-minimal KahlerK= ||

2

+k

||4

M2P

V kVinf

M2P

||2 k

k 1

New inflation in SUGRA Izawa Yanagida(1997)


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New inflation in SUGRA Izawa,Yanagida(1997)

W = v2 gn .

K= ||2 + k4

||4 1

Hybrid inflation in SUGRA

W = (v2 )

Dvali, Shafi,Schafer(1994)Linde,Riotto(1997)

K= ||2 + ||2

V v4 kv42 gv2n + g22n

V v4

1 +2

322ln2

2.

1-loop effective potential


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For large field model

Vexp

||2

M2P .

too steep for inflation

Shift symmetry + iC

can be inflation

K=

1

2(+

)2

Kawasaki,Yamaguchi,Yanagida(2000)

Shift symmetry breaking term

W = mX

V1

2m

22

Im[]

Chaotic inflation in SUGRA


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Use D-term

Halyo(96)Binetruy,Dvali (96)D-term inflation

W =

V g22 1 +g2

162ln

||2

2.

From D-term+1-loop effective potential

: 0,

: +1

,

: 1

hybrid inflation

D-term potential does not suffer these problems

Note : U(1) is broken after inflation

U(1)FI

K= ||2 + ||2 + ||2

Kazunori Nakayama- Gravitational wave background as a probe of reheating temperature of the Universe

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