Self accelerating universe from non-linear massive gravity
13
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:1206.2723 arXiv:1111.4107
description
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. - PowerPoint PPT Presentation
Transcript of Self accelerating universe from non-linear massive gravity
Self accelerating universe from non-linear massive gravity
Chunshan LinKavli IPMU, Univ of Tokyo
Based on collaborations withA.Emir Gumrukcuoglu & Shinji Mukohyama
arXiv:1109.3845
arXiv:1206.2723arXiv:1111.4107
Introduction
Cosmic acceleration
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
6 degrees of freedom
Helicity ±2, ±1, 0 5 dof？ 6th dof is the BD ghost!
Introduction • C. de Rham, G. Gabadadze and A. Tolly 2011
Source of MASS !
4 Stukelberg scalars respect Poincare symmetry
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)
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 Stukelberg scalars motivated by…
Minkowski metric
Open FRW chart
Both physical metric and fiducial metric respect FRW symmetry !
reads
• 1st solution
• 2nd and 3rd solutions
Please notice that these 2 solutions do not exist when K=0.
Self accelerating FRW universe
Freedmann equation
Self accelerating FRW universe
where
The effective cosmological constant
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 .
Self accelerating FRW universe
Sign of the effective cosmological constant
Ghost instability
See Emir’s talk after a little while
Break FRW symmetry
Some extended theories
Anisotropic FRW universe We are going to look for a health region with large anisotropy, and then
look for an attractor in this health region
Consider the simplest Bianchi I type metric
As for the fiducial metric
Varying the stuckelburg scalars
arXiv:1206.2723
Anisotropy
EoM of Stuckelburg scalar
Where
Einstein eqs
Where
Anisotropic FRW universe
Eintein Eqs EoM
Anisotropic FRW universe
Einstein Equations
+EoM Fixed points
Local Stability
Global Stability
Isotropic Fine Tuning
Non-trivial anisotropic
solution
Local stability condition
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
1isotropic universe
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!
