Cosmology and Black Holes with the Ghost Condensate Shinji - - PowerPoint PPT Presentation

Cosmology and Black Holes with the Ghost Condensate

Shinji Mukohyama (University of Tokyo)

Nima Arkani-Hamed Hsin-Chia Cheng Paolo Creminelli Markus Luty Jesse Thaler Toby Wiseman Matias Zaldarriaga with

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).

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.

Can we change gravity in IR to address these mysteries?

Very first step: is it even possible to modify gravity in IR in a theoretically consistent way?

Previous proposals

• Massive gravity
• Dvali-Gabadadze-Porrati model

) 4 ( 2 4 R

M

) 5 ( 3 5R

M

Infinite volume 5th dim.

) (r V

~ 4D for 5D for

,

c

r r <

c

r r >

c

r

3 5 2 4 / M

M

~

3+1 brane

) (

2 2 4 4 4 2

h h x d f R g x d M S

Pl

− + − =

∫ ∫

μν 2 4 2

/

Pl g

M f m ≈

Fierz-Pauli mass term

graviton mass

No predictability because of large quantum effects Look like 4D GR Modified gravity in IR Massive gravity & DGP brane model

1000km H0

• 1

length scale

Is it possible to modify gravity in the IR in a way that avoids the problem of macroscopic UV scale?

4D GR

lPl

Exactly 4D GR

length scale

No predictability

microscopic UV scale

Ghost condensation = Gravity in Higgs phase Higgs mechanism Symmetry breaking & Modifying force law K-inflation Inflation Cosmology Kinematically dominated Potentially dominated

Ghost condensation

Tachyons and Ghosts

Instability condense to a stable background Causality violation Sick Tachyon Field theory Particle mechanics More general framework Field theory Instability condense to a stable background Negative norm Sick Ghost Expectation

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

φ &

( )

2

) ( φ ∂ P Φ ( ) Φ V

Φ φ

μ

∂

2 2Φ

− m

2

φ & −

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 &

P φ &

2

M

Gravity (Hubble friction) drives you here! Attractor

φ φ ν

μ μν μν

∂ ∂ ′ + = ) ( ) (

4 4

M P g M P T

Exactly that of c.c. !

) (

4

M P −

Possible Applications: (I) Alternate origin for de Sitter phases in universe. * Acceleration today, with Λ=0. Cosmological observations alone can’t distinguish from C.C.! However, tiny Lorentz violation, spin- dependent long-range forces… Looks like matter- domination before it gets to dS phase! Dark matter? Need to see if it clumps properly Also dS dS Λ=0

(II) Qualitatively different picture of inflationary dS phase:

! ≠ 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

• eg. hybrid type

• cf. This is the reason why higher terms such as

are irrelevant at low E.

∫

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ∇ − L &

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 &

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

2 2

) ( M π π ∇ & non-G of ~

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ M H 1/4

scaling dim of op.

5 / 1

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ρ δρ

~

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

( )

5 / 1

/ ρ δρ ×

( )

ρ δρ /

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

1 3 1 2 6 1 3 2 1

, 1 ) , , ( k k k k F k k k k F

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

1 3 / k

k

1 2 / k

k

1 2 / k

k

1 3 / k

k

( )

2 2

5 3

G G NL G

f ς ς ς ς − ⋅ − =

1 2 / k

k 1

1 3 / k

k

What happens near a black hole?

• Ghost condensate
• defines a hypersurface orthogonal

congruence of timelike curves ~ observers

2 2 2

2 ) ( ) ( M X P L φ α ∇ − = φ φ

μ μ ∂

−∂ = X

→ ′ P

φ

μ μ

−∂ = u ≠ ∂ φ

μ

φ = const.

Observer 1 2 3 4

• cf. in early universe

μ

u

Mukohyama (in preparation)

Small tidal force Freely falling extended

• bjects

Zero Freely-falling pointlike

• bjects

Force Objects with Small corrections (for a large BH) P’=0 solution for α = 0 Zero for α = 0 Ghost condensate Accretion rate Could be huge Accelerated

• bjects

Could be huge

≠ ′ P

2 2 2

2 ) ( M φ α ∇

Myself A.Frolov Two different calculations by myself and A.Frolov

• Q1. Which is correct?
• A1. Both are correct in some sense since

both should give upper bounds for the late time accretion rate. But, the smaller upper bound is more useful.

• Q2. Why do they give upper bounds, not

lower bounds?

• A2. The system should settle to a

configuration with less backreaction and less accretion rate. Q&A for the two calculations

Black hole in the ghost condensate

An exact solution without α term: φ=M2τ Schwarzschild geometry in Gaussian coordinate

3 / 2 2 / 3

2 4 3 1 ) , ( ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ρ τ ρ τ m m a

2 ) 2 ( 2 2 2 2 2

) , ( ) , ( Ω + + − = d a a d d ds ρ τ ρ ρ τ ρ τ

With α term, this is no longer a solution. Accretion of ghost condensate into black hole Accretion rate suppressed by M2/Mpl2

) ( , 4 3 4 9

2 1 3 / 2 2 2 1

α α O m m m m t M M m m

MS pl

+ + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ≈

Asymptotic formula:

( 2 ) (

2

M X P α −

2

) φ

I have set in the lowest order in α because the Hubble friction during, say, inflation makes P’ vanish with extremely good accuracy ( ).

) ( ' = X P

3

'

−

∝ a P

If then we would obtain much larger accretion rate [A.Frolov] because .

) 1 ( ) ( ' O X P =

) ( '

4

X P M ≈

π

ρ

Anyway, this non-zero ρπ soon accretes to the black hole and P’(X) should relax to zero. If we set in the lowest order, then we

• btain a very small accretion rate suppressed by

M2/Mpl2.

) ( ' = X P

Summarizing:

Ghost condensate, new kind of fluid that does not dilute as universe expands. But not a C.C.! A real fluid with a real scalar excitation. Modification of linear gravity in IR:

• Anti gravity
• Oscillating forces
• Change at different length & time scales

Ghost inflation:

• Scale-invariant (n=1) perturbations
• Low H with sufficient quantum fluctuations
• Large non-Gaussianity

Even richer dynamics:

Arkani-Hamed, Cheng, Luty, Mukohyama and Wiseman (in preparation)

• Finite size effect
• Moving source, friction, frame dragging effect
• Non-linear dynamics, would-be caustics, bounce
• Large-scale structure of ether frame
• Accretion into a black hole

Mukohyama (in preparation)

More new results will come out! Gauged ghost condensation

Cheng, Luty, Mukohyama and Thaler (in preparation)

Final remark

• The most symmetric class of backgrounds for

gravity + field theory has maximal

symmetry: Minkowski, AdS, dS.

• dS in superstring theory was just recently

constructed by KKLT.

• GHOST CONDENSATION provides

the second most symmetric class of

backgrounds.

• Superstring construction wanted!

Lorents symmetry (Time translation) Gauge symmetry Spontaneous breaking Gravitational force Gauge force Modifying Oscillating Yukawa-type

New potential

P’=0, P’’>0 V’=0, V’’>0 Condensate Ghost Tachyon Instability Order Parameter Ghost Condensation Higgs Mechanism

φ &

( )

2

) ( φ ∂ P Φ ( ) Φ V

Φ φ

μ

∂

2 2Φ

− m

2

φ & −

Thank you very much for your listening!