Massive gravity and cosmology Shinji Mukohyama (YITP Kyoto) Based on collaboration with Antonio DeFelice, Garrett Goon, Emir Gumrukcuoglu, Lavinia Heisenberg, Kurt Hinterbichler, David Langlois, Chunshan Lin, Ryo Namba, Atsushi Naruko, Takahiro Tanaka, Norihiro Tanahashi, Mark Trodden
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Nonlinear massive gravity and Cosmologyseminar/pdf_2014_kouki/141028Mukohyama.pdfquasidilaton theory has ghost instability [Gumrukcuoglu, Hinterbichler, Lin, Mukohyama, Trodden 2013;
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Massive gravityand cosmology
Shinji Mukohyama(YITP Kyoto)
Based on collaboration with
Antonio DeFelice, Garrett Goon, Emir Gumrukcuoglu, Lavinia
Heisenberg, Kurt Hinterbichler, David Langlois, Chunshan Lin,
D’Amico, et.al. (2011)Non-existence of flatFRW (homogeneous isotropic) universe!
NEWNonlinear instability of
FRW solutionsDGM (2012)
Open universes with self-accelerationGLM (2011a)
More general fiducialmetric fmu
closed/flat/open FRW universes allowed
GLM (2011b)
GLM = Gumrukcuoglu-Lin-Mukohyama
DGM = DeFelice-Gumrukcuoglu-Mukohyama
Our recent contributionsCosmological solutions of nonlinear massive gravity
New class of cosmological solutionGumrukcuoglu, Lin, Mukohyama, arXiv: 1206.2723 [hep-th]
+ De Felice, arXiv: 1303.4154 [hep-th]• Healthy regions with (relatively) large anisotropy
• Are there attractors in healthy region?
• Classification of fixed points
• Local stability analysis
• Global stability analysis
At attractors, physical metric is isotropic but fiducial metric is anisotropic. Anisotropic FLRW universe!
statistical anisotropy expected(suppressed by small mg
2)
Anisotropy in
Expansion
Anisotropy in fiducial metric
New class of cosmological solutionGumrukcuoglu, Lin, Mukohyama, arXiv: 1206.2723 [hep-th]
+ De Felice, arXiv: 1303.4154 [hep-th]
Good? Bad?
GLM = Gumrukcuoglu-Lin-Mukohyama
DGM = DeFelice-Gumrukcuoglu-Mukohyama
Our recent contributionsCosmological solutions of nonlinear massive gravity
Quasidilaton• New nonlinear instability [DeFelice, Gumrukcuoglu,
Mukohyama 2012] (i) new backgrounds, or (ii) extended theories
• Quasidilaton: scalar s with global symmetry:
• Action
• Scaling solution = self-accelerating de Sitter(H = const > 0 with = 0)
D’Amico, Gabadadze, Hui, Pirtskhalava, 2012
Extension of quasidilaton
• Self-accelerating solution in the original quasidilaton theory has ghost instability[Gumrukcuoglu, Hinterbichler, Lin, Mukohyama, Trodden 2013; D’Amico, Gabadadze, Hui, Pirtskhalava 2013]
• Simple extension:
• Self-accel solution is stable within 5 d.o.f. if
arXiv: 1306.5502 [hep-th] /w A. De Felice
Bimetric theroy
• fmu dynamical [Hassan&Rosen 2011]
1 massless + 1 massive 2+5 = 7 d.o.f.
• Stable GR-like FLRW background
b/a const (mg2 >> r/Mp
2)
• Fine-tuning of parameters
small cc viable late-time cosmology
light mgw interesting gw phenomenology
large Vainshtein radius recovery of GR
De Felice, Nakamura, Tanaka, arXiv:1304.3920;
De Felice, Gumrukcuoglu, Mukohyama, Tanaka, Tanahashi, arXiv:1404.0008
Rotation-invariant massive gravity
• H ≠ 0 breaks Lorentz invariance but
preserves rotation-invariance
• Does mg ~ H have to preserve Lorentz
invariance?
• Rotation-invariant theoriesRubakov 2004, Dubovsky 2004, Blas et al 2009,