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

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 sun observed in 1800’s… mercury which people tried to vulcan sun explain with a “dark planet”, Vulcan, mercury 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 ∫ ∫ = − + − 2 4 4 4 2 2 S M d x g R f d x ( h h ) μν Pl m ≈ 2 4 2 f / M graviton mass g Pl Fierz-Pauli mass term • Dvali-Gabadadze-Porrati model Infinite volume 5th dim. 3+1 3 ( 5 ) 2 ( 4 ) M 5 R M 4 R brane r < r , r ~ V ( r ) 2 3 ~ 4D for M 4 / M c c 5 r > r 5D for c

Massive gravity & DGP brane model -1 1000km H 0 length scale No predictability Look like Modified gravity because of large 4D GR in IR quantum effects 4D GR predictability length scale No l Pl Exactly 4D GR microscopic UV scale Is it possible to modify gravity in the IR in a way that avoids the problem of macroscopic UV scale?

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

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

Higgs Mechanism Ghost Condensation Φ ∂ φ Order ( ) ( ) Φ ( φ ∂ 2 V μ P ) Parameter Φ & φ & − m 2 Φ − φ 2 2 Instability Tachyon Ghost Condensate V’=0, V’’>0 P’=0, P’’>0 Spontaneous Gauge symmetry Lorents symmetry breaking (Time translation) Modifying Gauge force Gravitational force New Yukawa-type Oscillating potential

For simplicity ( ) P = P ( φ ∂ 2 L ) φ in FRW background. & φ E.O.M. & ′ φ → ∞ & ′ → ∂ ⋅ φ = 3 a P 0 as [ a P ] 0 2 = t & ′ φ & φ = P ( ) 0 0 or (unstable ghosty background)

P 2 M & φ Gravity (Hubble friction) Attractor drives you here! ′ = + ∂ φ ν ∂ φ 4 4 T P ( M ) g P ( M ) μν μν μ − 4 P ( M ) Exactly that of c.c. !

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… Also Λ =0 Looks like matter- dS dS domination before it gets to dS phase! Dark matter? Need to see if it clumps properly

(II) Qualitatively different picture of inflationary dS phase: & φ ≠ Ghost Inflation 0 ! eg. hybrid type φ NOT SLOW ROLL scaling dim of π Scale-invariant perturbations δρ δπ H & ~ ~ ~ M ⋅ φ δπ 1 / 4 2 ( / ) H M M & ρ φ 5 / 4 ⎛ ⎞ H H ⎜ ⎟ ~ [compare ] ε ⎝ ⎠ M M Pl

→ E rE − → 1 ⎡ ⎤ dt r dt α ∇ π 2 2 1 ( ) Make ∫ π − + 3 & 2 L ⎢ ⎥ dtd x − → 2 ⎣ ⎦ invariant 2 M 1 / 2 dx r dx ′ − ∇ π 4 2 P ( M )( ) π → π 1 / 4 r Scaling dim of π is 1/4 ! not the same as the mass dim 1! cf. This is the reason why higher terms such as π ∇ π & 2 ( ) ∫ are irrelevant at low E. 3 dtd x ~ 2 M

Prediction of Large (visible) non-Gauss. π ∇ π & 2 ( ) Leading non-linear interaction 2 M 1/4 ⎛ ⎞ scaling dim of op. H ⎜ ⎟ non-G of ~ ⎝ ⎠ M 1 / 5 ⎛ ⎞ δρ ⎜ ⎟ ~ ⎜ ⎟ ρ ⎝ ⎠ ( ) × δρ / ρ 1 / 5 ~ 10 -2 . VISIBLE. [Really “0.1” Compare with usual inflation where ( ) non-G ~ ~ 10 -5 too small.] δρ / ρ

3-point function for ghost inflation ⎛ ⎞ 1 k k ⎜ ⎟ = 2 3 ( , , ) , F k k k F ⎜ ⎟ 1 2 3 6 ⎝ ⎠ k k k 1 1 1 k 2 / k k 3 / k k 2 / k 1 1 1 k 3 / k 1 1 3-point function for “local” non-G ( ) 3 ς = ς − ⋅ ς − ς 2 2 f G NL G G 5 k 2 / k 1 k 3 / k 1

What happens near a black hole? Mukohyama (in preparation) μ ∂ α ∇ φ 2 2 ( ) = −∂ φ φ = − X L P ( X ) μ 2 2 M ′ → cf. in early universe P 0 ∂ φ ≠ • Ghost condensate 0 μ μ μ = −∂ φ • defines a hypersurface orthogonal u congruence of timelike curves ~ observers μ u φ = const. Observer 1 2 3 4

Two different calculations by myself and A.Frolov Objects Force Accretion Ghost rate condensate Freely-falling Zero Zero P’=0 solution for α = 0 for α = 0 pointlike Myself objects Small with Freely falling Small tidal α ∇ φ 2 2 corrections ( ) extended force (for a large objects 2 2 M BH) A.Frolov Accelerated Could be Could be ′ ≠ P 0 objects huge huge

Q&A for the two calculations • 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.

Black hole in the ghost condensate Schwarzschild geometry in Gaussian coordinate ρ 2 d = − τ + + ρ τ ρ Ω 2 2 2 2 2 ds d a ( , ) d τ ρ ( 2 ) a ( , ) 2 / 3 ⎡ ⎤ 3 / 2 ⎛ ⎞ τ 3 2 m τ ρ = ⎢ − ⎜ ⎟ ⎥ 0 a ( , ) 1 ⎜ ⎟ ρ ⎢ ⎝ ⎠ ⎥ 4 m ⎣ ⎦ 0 An exact solution without α term: φ =M 2 τ

With α term, this is no longer a solution. Accretion of ghost condensate into black hole Accretion rate suppressed by M 2 /M pl2 Asymptotic formula: 2 / 3 ⎛ ⎞ 2 m 9 M 3 t ⎜ ⎟ ≈ = + α + α 2 1 , m m m O ( ) ⎜ ⎟ MS 0 1 2 ⎝ ⎠ 4 4 m M m 0 0 pl α − φ 2 P ( X ) ( ) 2 2 M

I have set in the lowest order in α because = P ' ( X ) 0 the Hubble friction during, say, inflation makes P’ − ∝ a 3 vanish with extremely good accuracy ( ). P ' = P ' ( X ) O ( 1 ) If then we would obtain much larger ρ ≈ 4 M P ' ( X ) accretion rate [A.Frolov] because . π Anyway, this non-zero ρ π soon accretes to the black hole and P’(X) should relax to zero. = If we set in the lowest order, then we ' ( ) 0 P X obtain a very small accretion rate suppressed by M 2 /M pl2 .

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!

Higgs Mechanism Ghost Condensation Φ ∂ φ Order ( ) ( ) Φ ( φ ∂ 2 V μ P ) Parameter Φ & φ & − m 2 Φ − φ 2 2 Instability Tachyon Ghost Condensate V’=0, V’’>0 P’=0, P’’>0 Spontaneous Gauge symmetry Lorents symmetry breaking (Time translation) Modifying Gauge force Gravitational force New potential Yukawa-type Oscillating Thank you very much for your listening!