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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.
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Can we change gravity in IR? Change Theory? (eg. Massive gravity, DGP model)
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Need UV completion Look like 4D GR Modified gravity in IR Massive gravity & DGP model 1000kmH 0 -1 length scale 4D GR l Pl Exactly 4D GR length scale Need UV completion microscopic UV scale
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Can we change gravity in IR? Change Theory? (eg. Massive gravity, DGP model) Macroscopic UV scales Cannot be decoupled Change State? Higgs phase of gravity The simplest: Ghost condensation Arkani-Hamed, Cheng, Luty and Mukohyama, JHEP 0405:074,2004.
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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!
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Ghost condensation 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 Arkani-Hamed, Cheng, Luty and Mukohyama, JHEP 0405:074,2004
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Bounds on symmetry breaking scale M M Jeans Instability (sun) 100GeV1TeV Supernova time-delay ruled out 0 allowed Twinkling from Lensing (CMB) So far, there is no conflict with experiments and observations if M < 100GeV. Arkani-Hamed, Cheng, Luty and Mukohyama and Wiseman, JHEP 0701:036,2007
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Higgs mechanismGhost condensate Order parameter InstabilityTachyonGhost CondensateV’=0, V’’>0P’=0, P’’>0 Broken symmetry Gauge symmetryTime translational symmetry Force to be modified Gauge forceGravity New force law Yukawa typeNewton+Oscillation
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For simplicity EOM is or Ghosty in FRW universe Ghost condensate is an attractor!
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DM like component DE like component Condensate Present value =0 Can be an alternative to DE and DM? Usual Higgs mechanism =0 Yes, at least for FRW background! “OK” for linear perturbation! Very interesting non-linear dynamics
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redshift effective m B Linear Perturbation H(z) & vis (z) Input Output Higgs sector Lagrangian Geometrical properties Dynamical properties Mukohyama, JCAP 0610:011,2006. Compare! Linear perturbation equation
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Simplest case Exact shift symmetry, i.e. no potential May be called GDM. (FRW evolution is exactly like CDM.) Linear perturbation equation (derived using the formalism in Mukohyama, JCAP 0610:011,2006)
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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 < 100GeV. Behaves like DE+DM for FRW background and large-scale linear perturbation. The simplest case is GDM. Cosmological perturbation may distinguish ghost condensation from DE/DM.
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Higgs mechanismGhost condensate Order parameter InstabilityTachyonGhost CondensateV’=0, V’’>0P’=0, P’’>0 Broken symmetry Gauge symmetryTime translational symmetry Force to be modified Gauge forceGravity New force law Yukawa typeNewton+Oscillation Thank you very much!
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