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 Mukohyama and Wiseman, hep-ph/0507120 Cheng, Luty, Mukohyama and Thaler, hep-th/0603010 Mukohyama, hep-th/0502189, hep-th/0607181, hep-th/0610254

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? � 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

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 V ’ =0, V ’’ >0 P ’ =0, P ’’ >0 Condensate Spontaneous Gauge symmetry Lorents symmetry breaking (Time translation) Modifying Gauge force Gravitational force New Yukawa-type Oscillating in space potential Growing in time

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)

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 V ’ =0, V ’’ >0 P ’ =0, P ’’ >0 Condensate Spontaneous Gauge symmetry Lorents symmetry breaking (Time translation) Modifying Gauge force Gravitational force New Yukawa-type Oscillating in space potential Growing in time

Systematic construction of Low- energy effective theory Backgrounds characterized by ∂ φ ≠ � 0 and timelike μ � Background metric is maximally symmetric, either Minkowski or dS.

� π ≡ δφ = φ = 0 ( , ) . t x t Gauge choice: (Unitary gauge) � � � ′ → x x ( x t , ) Residual symmetry: Write down most general action invariant under this residual symmetry. ( Action for π : undo unitary gauge!) = η + g h Start with flat background μν μν μν δ = ∂ ξ + ∂ ξ h μν μ ν ν μ Under residual ξ i δ = δ = ∂ ξ δ = ∂ ξ + ∂ ξ h 0 , h , h 00 0 i 0 i ij i j j i

ξ i Action invariant under ξ i Action invariant under ( ) 2 h OK ( ) 00 1 = ∂ − ∂ − ∂ ( ) K h h h 2 h ij 0 ij j 0 i i 0 j 2 0 i 2 , ij OK K K K ij α α ⎧ ⎫ ( ) = + 2 − − + � 4 ⎨ 2 ij ⎬ 1 2 L L M h K K K eff EH 00 ij ⎩ ⎭ 2 2 M M π Action for π Action for → − ∂ π ξ 0 = π h h 2 00 00 0 → + ∂ ∂ π K K ij ij i j � α ⎧ ( ) ( ) 2 = + − π 2 − + ∇ π � 4 ⎨ 2 1 L L M h 2 K eff EH 00 ⎩ 2 M � � � � α ⎫ ( )( ) − + ∇ ∇ π + ∇ ∇ π + � ij i j ⎬ 2 K K ij i j ⎭ 2 M

� α ⎧ ( ) ( ) 2 = + − π 2 − + ∇ π � 4 2 ⎨ 1 L L M h 2 K eff EH 00 ⎩ 2 M � � � � α ⎫ ( )( ) − + ∇ ∇ π + ∇ ∇ π + � ij i j ⎬ 2 K K ij i j ⎭ 2 M Dispersion relation Dispersion relation α ω = 2 4 k 2 term is forbidden by symmetry 2 k M Coupling to gravity α α 2 M ω = − 2 4 2 k k O(M 2 /M Pl 2 ) correction 2 2 M 2 M Pl Jeans- -like (IR) instability like (IR) instability Jeans ω 2 < 0 for k < k c = M 2 /2M pl r J ~ M pl /M 2 , t J ~ M pl 2 /M 3

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 V ’ =0, V ’’ >0 P ’ =0, P ’’ >0 Condensate Spontaneous Gauge symmetry Lorents symmetry breaking (Time translation) Modifying Gauge force Gravitational force New Yukawa-type Oscillating in space potential Growing in time

Bounds on symmetry breaking scale M Arkani-Hamed, Cheng, Luty and Mukohyama and Wiseman, hep-ph/0507120 0 100GeV 1TeV M allowed ruled out Jeans Instability (sun) ruled out Twinkling from Lensing (CMB) ruled out Supernova time-delay c.f. Gauged ghost condensation allows much higher M (M < 10 12 GeV) Cheng, Luty, Mukohyama and Thaler, hep-th/0603010

Applications to Cosmology (I) Ghost Inflation Ghost Inflation � φ ≠ 0 ! Arkani-Hamed, Creminelli, Mukohyama and Zaldarriaga hep-th/0312100 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 � φ ρ 5 / 4 ⎛ ⎞ H H ⎜ ⎟ ~ [compare ] ε ⎝ ⎠ M M Pl

→ E rE − → 1 ⎡ ⎤ dt r dt α ∇ π 2 2 1 ( ) Make ∫ π − + � � 3 2 ⎢ ⎥ 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 / k k / k k / k 2 1 3 1 2 1 k / k 1 3 1 3-point function for “local” non-G ( ) 3 ς = ς − ⋅ ς − ς 2 2 f G NL G G 5 k / k 2 1 k / k 3 1

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 . ( ) ( ) Φ ∂ φ 2 V P ( ) Usual Higgs mechanism Ghost condensation Λ =0 Φ Λ =0 Λ < Λ < 0 0 eff eff Λ eff >0 CDM dS dS • Clustering properties remain unexplored and may be different from c.c. + CDM.

Cosmic Uroboros Uroboros Cosmic Higgs phase Higgs phase DE/DM DE/DM of gravity of gravity String/M theory? String/M theory?

KKLT setup KKLT setup 10D = 4D universe x 6D internal space CY CY Shape & Volume Shape & Volume stabilized stabilized Warped Throat Warped Throat Anti-D3-branes Non-SUSY NS5-brane Kachru, Pearson & Verlinde (2002)

Correspondence principle Correspondence principle Horowitz & Polchinski (1997) Stringy Stringy Black- -Brane Brane Black Object Object Size > R grav Size < R grav Non- -SUSY SUSY Non Black- -Brane Brane Black NS5- -brane brane NS5 ( ) 2 > M RR : # of R-R flux � M / N g N 1 ∼ : # of ‘s N D 3 RR 3 s 3 3 g s : string coupling Mukohyama, hep-th/0610254

Black brane brane at the tip at the tip Black Universe ⊗ 4D Non- -extremal extremal Non black 3- -brane brane black 3

Spontaneous Lorentz breaking Spontaneous Lorentz breaking • The (3+1)-dim spacetime is spanned by ( t , x i ). Warp factors for the tt-component and x i the ij-components t black 3-brane are different. Non-extremal Projection onto t = const. surfaces Spontaneous Lorentz breaking! t x i r = const. Gauged Ghost Condensation Projection onto r x i = const. surfaces

GL instability • Non-extremal Black branes are gravitationally unstable. [Gregory-Laflamme, PRL70, 2837 (1993); NPB428, 399 (1994)]

• The dispersion relation is similar to that for 2 < g c 2 . the NG boson in our setup with g GCC Charged black string with r + =2 − ω = 2 � = 2 k [Gregory-Laflamme, NPB428, 399 (1994)]

• 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. Conjecture Conjecture Mukohyama, hep-th/0610254 Low-E EFT: Jeans-like instability DUAL Geometrical: GL instability

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 ( ) 2 > � M / N g N 1 ∼ RR 3 s 3 is a UV completion (string theory version) of the gauged ghost condensation.