Gravity in Higgs phase Shinji Mukohyama IPMU U
- Slides: 14
Gravity in Higgs phase Shinji Mukohyama IPMU, U of Tokyo • Arkani-Hamed, Cheng, Luty and Mukohyama, JHEP 0405: 074, 2004. • Arkani-Hamed, Cheng, Luty and Mukohyama and Wiseman, JHEP 0701: 036, 2007. • Mukohyama, JCAP 0610: 011, 2006.
Can we change gravity in IR? ØChange Theory? (eg. Massive gravity, DGP model)
Massive gravity & DGP model 1000 km Need UV completion H 0 -1 Look like 4 D GR length scale Modified gravity in IR 4 D GR Need UV completion l. Pl microscopic UV scale length scale Exactly 4 D GR
Can we change gravity in IR? Ø Change Theory? (eg. Massive gravity, DGP model) Macroscopic UV scales Cannot be decoupled ØChange State? Higgs phase of gravity The simplest: Ghost condensation Arkani-Hamed, Cheng, Luty and Mukohyama, JHEP 0405: 074, 2004.
Higgs mechanism • Spontaneously breaks gauge symmetry. (Theory itself has gauge symmetry. ) • Gives mass to gauge boson. • Changes Gauss law to Yukawa law! • Can describe weak interaction!
Ghost condensation Arkani-Hamed, Cheng, Luty and Mukohyama, JHEP 0405: 074, 2004 • Spontaneously breaks Lorentz symmetry. (Theory itself has Lorentz symmetry. ) • Gives “mass” to graviton. • Adds oscillating time-dependent potential to Newton potential! (But the time scale is very long. ) = Higgs phase of gravity
Bounds on symmetry breaking scale M Arkani-Hamed, Cheng, Luty and Mukohyama and Wiseman, JHEP 0701: 036, 2007 0 100 Ge. V allowed Jeans Instability (sun) Twinkling from Lensing (CMB) Supernova time-delay 1 Te. V ruled out So far, there is no conflict with experiments and observations if M < 100 Ge. V. M
Higgs mechanism Ghost condensate Order parameter Instability Tachyon Ghost Condensate V’=0, V’’>0 P’=0, P’’>0 Broken Gauge symmetry Force to be Gauge force modified New force Yukawa type law Time translational symmetry Gravity Newton+Oscillation
For simplicity in FRW universe Ghost condensate is an attractor! EOM is or Ghosty
Can be an alternative to DE and DM? Usual Higgs mechanism Yes, at least for L=0 FRW background! L=0 “OK” for linear perturbation! Present value DE like DM like component interesting component Very non-linear dynamics Condensate
Input H(z) & rvis(z) effective m. B Linear Perturbation Geometrical properties Mukohyama, JCAP 0610: 011, 2006. Output Higgs sector Lagrangian Linear perturbation equation Compare! Dynamical properties redshift
Simplest case • Exact shift symmetry, i. e. no potential • May be called LGDM. (FRW evolution is exactly like LCDM. ) • Linear perturbation equation (derived using the formalism in Mukohyama, JCAP 0610: 011, 2006)
Summary • Ghost condensation is the simplest Higgs phase of gravity. • The low-E EFT is determined by the symmetry breaking pattern. No ghost in the EFT. • Gravity is modified in IR. • Consistent with experiments and observations if M < 100 Ge. V. • Behaves like DE+DM for FRW background and large-scale linear perturbation. • The simplest case is LGDM. • Cosmological perturbation may distinguish ghost condensation from DE/DM.
Higgs mechanism Ghost condensate Order parameter Thank you very much! Instability Tachyon Ghost Condensate V’=0, V’’>0 P’=0, P’’>0 Broken Gauge symmetry Force to be Gauge force modified New force Yukawa type law Time translational symmetry Gravity Newton+Oscillation
