Higgs Phase of Gravity Shinji Mukohyama (University of Tokyo) - - PowerPoint PPT Presentation

higgs phase of gravity
SMART_READER_LITE
LIVE PREVIEW

Higgs Phase of Gravity Shinji Mukohyama (University of Tokyo) - - PowerPoint PPT Presentation

Higgs Phase of Gravity Shinji Mukohyama (University of Tokyo) December 12, 2006 @ IHP Arkani-Hamed, Cheng, Luty and Mukohyama, hep-th/0312099 Arkani-Hamed, Creminelli, Mukohyama and Zaldarriaga, hep-th/0312100 Arkani-Hamed, Cheng, Luty and


slide-1
SLIDE 1

Higgs Phase of Gravity

Shinji Mukohyama (University of Tokyo) December 12, 2006 @ IHP

Arkani-Hamed, Cheng, Luty and Mukohyama, hep-th/0312099 Arkani-Hamed, Creminelli, Mukohyama and Zaldarriaga, hep-th/0312100 Arkani-Hamed, Cheng, Luty and Mukohyama and Wiseman, hep-ph/0507120 Cheng, Luty, Mukohyama and Thaler, hep-th/0603010 Mukohyama, hep-th/0502189, hep-th/0607181, hep-th/0610254

slide-2
SLIDE 2

Motivation

  • Gravity at long distances

Flattening galaxy rotation curves Dimming supernovae accelerating universe

  • Usual explanation: new forms of matter

(DARK MATTER) and energy (DARK ENERGY).

slide-3
SLIDE 3

Historical remark:

Precession of perihelion

  • bserved in 1800’s…

mercury

sun

which people tried to explain with a “dark planet”, Vulcan,

mercury

vulcan sun But the right answer wasn’t “dark planet”, it was “change gravity” from Newton to GR.

slide-4
SLIDE 4

Can we change gravity in IR to address these mysteries?

Change theory? Macroscopic UV scale… Change state (phase)? Higgs phase of gravity The simplest: Ghost Condensation

Arkani-Hamed, Cheng, Luty and Mukohyama, hep-th/0312099

slide-5
SLIDE 5

Higgs Mechanism Ghost Condensation Order Parameter Instability Tachyon Ghost Condensate V’=0, V’’>0 P’=0, P’’>0 Spontaneous breaking Gauge symmetry Lorents symmetry (Time translation) Modifying Gauge force Gravitational force New potential Yukawa-type Oscillating in space Growing in time

φ

  • (

)

2

) ( φ ∂ P Φ ( ) Φ V

Φ φ

μ

2 2Φ

− m

2

φ

slide-6
SLIDE 6

For simplicity

( )

2

) ( φ

φ

∂ = P L

P in FRW background. E.O.M.

] [

3

= ⋅ ′ ∂ φ

  • P

a

t

→ ′φ

  • P

as

∞ → a = φ

  • r

) (

2 =

′ φ

  • P

(unstable ghosty background)

φ

slide-7
SLIDE 7

Higgs Mechanism Ghost Condensation Order Parameter Instability Tachyon Ghost Condensate V’=0, V’’>0 P’=0, P’’>0 Spontaneous breaking Gauge symmetry Lorents symmetry (Time translation) Modifying Gauge force Gravitational force New potential Yukawa-type Oscillating in space Growing in time

φ

  • (

)

2

) ( φ ∂ P Φ ( ) Φ V

Φ φ

μ

2 2Φ

− m

2

φ

slide-8
SLIDE 8
  • and timelike

Background metric is maximally symmetric, either Minkowski or dS. Systematic construction of Low- energy effective theory Backgrounds characterized by

≠ ∂ φ

μ

slide-9
SLIDE 9

Gauge choice:

. ) , ( t x t =

  • φ

(Unitary gauge)

) , ( x t x x

Residual symmetry:

Write down most general action invariant under this residual symmetry. ( Action for π: undo unitary gauge!) Start with flat background

μν μν μν

η h g + =

μ ν ν μ μν

ξ ξ δ ∂ + ∂ = h

i

Under residual ξ

i j j i ij i i

h h h ξ ξ δ ξ δ δ ∂ + ∂ = ∂ = = , ,

00

π δφ ≡ =

slide-10
SLIDE 10

Action invariant under Action invariant under ξ ξi

i

( )

2 00

h

( )

2 0i

h

2, ij ij

K K K

( )

1 2

ij ij j i i j

K h h h = ∂ − ∂ − ∂

OK OK

( )

2 4 2 1 2 00 2 2 ij eff EH ij

L L M h K K K M M α α ⎧ ⎫ = + − − + ⎨ ⎬ ⎩ ⎭

  • Action for

Action for π π

ij ij i j

K K π → + ∂ ∂

00 00

2 h h π → − ∂

ξ0 = π

( )

( )

2 2 4 2 1 00 2

2

eff EH

L L M h K M α π π ⎧ = + − − + ∇ ⎨ ⎩

  • (

)( )

2 2 ij i j ij i j

K K M α π π ⎫ − + ∇ ∇ + ∇ ∇ + ⎬ ⎭

slide-11
SLIDE 11

Dispersion relation Dispersion relation

2 4 2 k

M α ω = ( )

( )

2 2 4 2 1 00 2

2

eff EH

L L M h K M α π π ⎧ = + − − + ∇ ⎨ ⎩

  • (

)( )

2 2 ij i j ij i j

K K M α π π ⎫ − + ∇ ∇ + ∇ ∇ + ⎬ ⎭

  • 2

2 4 2 2

2

Pl

M k k M M α α ω = −

2

Coupling to gravity k2 term is forbidden by symmetry O(M2/MPl

2) correction

Jeans Jeans-

  • like (IR) instability

like (IR) instability

ω2 < 0 for k < kc = M2/2Mpl

rJ ~ Mpl/M2, tJ ~ Mpl

2/M3

slide-12
SLIDE 12

Higgs Mechanism Ghost Condensation Order Parameter Instability Tachyon Ghost Condensate V’=0, V’’>0 P’=0, P’’>0 Spontaneous breaking Gauge symmetry Lorents symmetry (Time translation) Modifying Gauge force Gravitational force New potential Yukawa-type Oscillating in space Growing in time

φ

  • (

)

2

) ( φ ∂ P Φ ( ) Φ V

Φ φ

μ

2 2Φ

− m

2

φ

slide-13
SLIDE 13

Bounds on symmetry breaking scale M

M

Jeans Instability (sun) 100GeV 1TeV Supernova time-delay ruled out ruled out ruled out

allowed

Twinkling from Lensing (CMB) Arkani-Hamed, Cheng, Luty and Mukohyama and Wiseman, hep-ph/0507120

c.f. Gauged ghost condensation allows much higher M (M < 1012 GeV)

Cheng, Luty, Mukohyama and Thaler, hep-th/0603010

slide-14
SLIDE 14

Applications to Cosmology (I)

! ≠ φ

  • φ

NOT SLOW ROLL Scale-invariant perturbations

ρ δρ φ δπ

  • H

~

δπ

4 / 1

) / ( M H M ⋅

~

4 / 5

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ M H φ ~

2

~

M

scaling dim of π [compare ]

ε

Pl

M H

Ghost Inflation Ghost Inflation

  • eg. hybrid type

Arkani-Hamed, Creminelli, Mukohyama and Zaldarriaga hep-th/0312100

slide-15
SLIDE 15
  • cf. This is the reason why higher terms such as

are irrelevant at low E.

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ∇ −

  • 2

2 2 2 3

) ( 2 1 M x dtd π α π

π π

4 / 1 2 / 1 1

r dx r dx dt r dt rE E → → → →

− −

Make invariant

Scaling dim of π is 1/4! not the same as the mass dim 1!

2 4

) )( ( π ∇ ′ − M P

2 2 3

~ ) ( M x dtd π π

slide-16
SLIDE 16

Prediction of Large (visible) non-Gauss. Leading non-linear interaction

2 2

( ) M π π ∇

  • non-G of ~

H M ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ 1/4

scaling dim of op.

1/5

δρ ρ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

~

[Really “0.1” ~ 10-2. VISIBLE. Compare with usual inflation where non-G ~ ~ 10-5 too small.]

( )

1/5

/ δρ ρ ×

( )

/ δρ ρ

slide-17
SLIDE 17

3 2 1 2 3 6 1 1 1

1 ( , , ) , k k F k k k F k k k ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

3-point function for ghost inflation 3-point function for “local” non-G

3 1

/ k k

2 1

/ k k

2 1

/ k k

3 1

/ k k

( )

2 2

3 5

G NL G G

f ς ς ς ς = − ⋅ −

2 1

/ k k 1

3 1

/ k k

slide-18
SLIDE 18

Cosmological Application (II)

Alternative to DE/DM Alternative to DE/DM

  • For FRW universe, it behaves like c.c. + CDM

behaves like c.c. + CDM.

  • Clustering properties remain unexplored and

may be different from c.c. + CDM.

dS dS Λ=0

Ghost condensation

Φ ( ) Φ V

Usual Higgs mechanism

eff

Λ <

eff

Λ <

Λ=0

( )

2

( ) P φ ∂

Λeff>0 CDM

slide-19
SLIDE 19

Cosmic Cosmic Uroboros Uroboros

DE/DM DE/DM

String/M theory? String/M theory?

Higgs phase Higgs phase

  • f gravity
  • f gravity
slide-20
SLIDE 20

KKLT setup KKLT setup

Anti-D3-branes Warped Throat Warped Throat 10D = 4D universe x 6D internal space CY CY Shape & Volume Shape & Volume stabilized stabilized Non-SUSY NS5-brane

Kachru, Pearson & Verlinde (2002)

slide-21
SLIDE 21

Correspondence principle Correspondence principle Stringy Stringy Object Object Black Black-

  • Brane

Brane

Size > Rgrav Size < Rgrav

Horowitz & Polchinski (1997)

Black Black-

  • Brane

Brane Non Non-

  • SUSY

SUSY NS5 NS5-

  • brane

brane

( )

2 3 3

/ 1

RR s

M N g N >

MRR: # of R-R flux : # of ‘s gs : string coupling

3

N 3 D

Mukohyama, hep-th/0610254

slide-22
SLIDE 22

Black Black brane brane at the tip at the tip

Non Non-

  • extremal

extremal black 3 black 3-

  • brane

brane

4D Universe ⊗

slide-23
SLIDE 23

Spontaneous Lorentz breaking Spontaneous Lorentz breaking

  • The (3+1)-dim spacetime is spanned by

( t , xi ). Non-extremal black 3-brane

Projection onto t = const. surfaces Projection onto xi = const. surfaces

r

r = const.

xi t

xi t

Warp factors for the tt-component and the ij-components are different.

Spontaneous Lorentz breaking!

Gauged Ghost Condensation

slide-24
SLIDE 24

GL instability

  • Non-extremal Black branes are gravitationally
  • unstable. [Gregory-Laflamme, PRL70, 2837

(1993); NPB428, 399 (1994)]

slide-25
SLIDE 25
  • The dispersion relation is similar to that for

the NG boson in our setup with gGCC

2 < gc 2.

[Gregory-Laflamme, NPB428, 399 (1994)]

2

ω − =

2

k =

  • Charged black string

with r+=2

slide-26
SLIDE 26
  • In our geometrical setup there is a black

brane at the bottom of the warped throat.

  • The world-volume of the black brane is

parallel to our world.

Geometrical: GL instability Low-E EFT: Jeans-like instability

DUAL Conjecture Conjecture

Mukohyama, hep-th/0610254

slide-27
SLIDE 27

Summary Summary

  • Ghost condensation is the simplest Higgs

phase of gravity, including only one Nambu- Goldstone boson. No ghost included.

  • Can drive inflation.
  • Can be alternative to DE/DM.
  • The KKLT setup in the regime of parameters

is a UV completion (string theory version) of the gauged ghost condensation.

( )

2 3 3

/ 1

RR s

M N g N >

slide-28
SLIDE 28

Higgs Mechanism Ghost Condensation Order Parameter Instability Tachyon Ghost Condensate V’=0, V’’>0 P’=0, P’’>0 Spontaneous breaking Gauge symmetry Lorents symmetry (Time translation) Modifying Gauge force Gravitational force New potential Yukawa-type Oscillating in space Growing in time

φ

  • (

)

2

) ( φ ∂ P Φ ( ) Φ V

Φ φ

μ

2 2Φ

− m

2

φ