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Self accelerating universe from non-linear massive gravity

Self accelerating universe from non-linear massive gravity. Chunshan Lin Kavli IPMU, Univ of Tokyo Based on collaborations with A.Emir Gumrukcuoglu & Shinji Mukohyama.  arXiv:1109.3845. arXiv:1111.4107. arXiv:1206.2723. Introduction . Cosmic acceleration. Introduction.

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Self accelerating universe from non-linear massive gravity

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  1. Self accelerating universe from non-linear massive gravity Chunshan Lin Kavli IPMU, Univof Tokyo Based on collaborations with A.EmirGumrukcuoglu & Shinji Mukohyama  arXiv:1109.3845 arXiv:1111.4107 arXiv:1206.2723

  2. Introduction Cosmic acceleration

  3. Introduction • Can we give graviton a mass? • Fierz and Pauli 1939 • Vainshtein 1972 non–linear interactions • Boulware–Deser (BD) ghost 1972 van Dam–Veltman–Zakharov discontinuity Lack of Hamiltonian constrain and momentum constrain 6th dof is the BD ghost! 6 degrees of freedom ？ 5 dof Helicity ±2, ±1, 0

  4. Introduction • C. de Rham, G. Gabadadzeand A. Tolly 2011 4 Stukelberg scalars respect Poincare symmetry Source of MASS ! Eliminate a helicity-0 mode, the so called BD ghost in the decoupling limit. It is also BD ghost free away from decoupling limit. (Hassan & Rosen 2011)

  5. Self accelerating FRW universe • No go result for FRW solution (G. D’Amico et al 2011 Aug.) • However… (A.Gumrukcuoglu, C. Lin, S. Mukohyama: 1109.3845) It does not extend to open FRW universe The 4 Stukelbergscalars motivated by… Minkowski metric Open FRW chart Both physical metric and fiducial metric respect FRW symmetry !

  6. Self accelerating FRW universe • reads • 1st solution • 2nd and 3rd solutions Please notice that these 2 solutions do not exist when K=0.

  7. Self accelerating FRW universe • Freedmann equation where The effective cosmological constant

  8. Self accelerating FRW universe • Break FRW symmetry • Some extended theories • Poincare Symmetry (arXiv:1111.4107) FRW symmetry in field space Flat/Open/Closed self-accelerating FRW universe is allowed with the same effective c.c . Ghost instability See Emir’s talk after a little while Sign of the effective cosmological constant

  9. Anisotropic FRW universe arXiv:1206.2723 • We are going to look for a health region with large anisotropy, and then look for an attractor in this health region Considerthe simplest Bianchi I type metric As for the fiducial metric Varying the stuckelburg scalars Anisotropy

  10. Anisotropic FRW universe • EoM of Stuckelburg scalar Where Einstein eqs EinteinEqs EoM Where

  11. Anisotropic FRW universe Isotropic Fine Tuning Non-trivial anisotropic solution Einstein Equations +EoM Fixed points Local Stability Global Stability Local stability condition

  12. Anisotropic FRW universe • We consider an example with For which local stability condition is satisfied. There is only one set of solution to 3 eqns of fixed point: • Remarks: • Anisotropy differs from GR; • Ghost free around fixed point; • Coordinates redefinition • Anisotropy cosmological • perturbation spectrum isotropic universe 1

  13. Summary • We introduce such two cosmological solutions in this talk: • Self-accelerating FRW universe; • Anisotropic FRW universe more exciting work is in progress…… full analyse on the perturbations of the attractor solution, observational effect… Thank you!

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