cosmology of ghost-free - centre for theoretical cosmologycosmo 2013 / cambridge / september 5, 2013...
TRANSCRIPT
Yashar Akrami
COSMO 2013 / Cambridge / September 5, 2013
Postdoctoral Fellow Institute of Theoretical Astrophysics University of Oslo, Norway
with: Tomi S. Koivisto, David F. Mota & Marit Sandstad
Cosmology of Ghost-free Bimetric Gravity:
Late-time Acceleration and Double-coupling Generalization
Accelerated expansion from ghost-free bigravity: a statistical analysis with improved generality JHEP 1303 (2013) 099 [arXiv:1209.0457]
& Bimetric gravity doubly coupled to matter: theory and cosmological implications
arXiv:1306.0004, to be submitted to JCAP
Fierz & Pauli (1939):
Demand for Massive Gravity
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The only ghost-free mass term:
(linearized metric fluctuations around flat space-time)
Consistent Non-linear Completion? Theoretically challenging, cosmologically interesting.
2011: breakthrough
de Rham & Gabadadze [arXiv:1007.0443] de Rham, Gabadadze & Tolley [arXiv:1011.1232] Hassan & Rosen [arXiv:1103.6055]
[arXiv:1106.3344] [arXiv:1109.3515] [arXiv:1111.2070]
Hassan, Rosen & Schmidt-May [arXiv:1109.3230]
• The only ghost-free, massive gravity
• The only ghost-free, bimetric gravity
A natural IR-modification of gravity: give mass to gravitons
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 2
Action:
Bimetric Theory of Gravity
Hassan-Rosen bimetric gravity based on de-Rham-Gabadadze-Tolley massive gravity:
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• gives dynamics to f • absent in dRGT massive gravity • dRGT massive gravity:
• No FLRW solutions when background metric is flat
• New nonlinear ghost instabilities if both FLRW
• Way out: anisotropic background metric, varying mass and quasi-dilaton extensions
• Superluminal effects
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 3
Isotropic and Homogeneous Universe
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Metrics:
Evolution:
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 4
Observational Constraints
Scanning Method:
Model Parameter: B0, B1, B2, B3, B4, Ωm0
(no Ωϒ, no curvature)
(B0=0)
State-of-the-art scanning algorithm: MultiNest (nested sampling): MCMC-like (both Bayesian and frequentist statistics)
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DL, DV, DA, H(z)
Data:
1. Luminosity distances from Type Ia SNe: 580 points (Union 2.1)
2. Position of the 1st CMB power-spectrum peak (angular scale
of sound horizon at recombination era): 1 point (WMAP 7)
3. BAO: Ratio of sound horizon scale at drag epoch to dilation scale: 6 points (2dFGRS, 6dFGS, SDSS and WiggleZ)
4. Constraints on H0: 1 point
(purely background)
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 5
Only B1 and Ωm0 nonzero
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Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 6
Only B1 and Ωm0 nonzero
Graviton Mass: m2 = 1.45 H0
2 ± 0.25 H02
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Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 7
Only B1 and Ωm0 nonzero
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Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 8
Only B1 and Ωm0 nonzero
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ΩΛ = B1y
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 9
Full Results
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• No exact ΛCDM without explicit cosmological constant (vacuum energy) • Dynamical dark energy • Degeneracies between parameters
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 10
Generalization: doubly coupled bigravity
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Action
Dust-dominated universe: Shown to be theoretically consistent
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 11
• So far, by proper semantics: “gravity coupled to matter and a symmetric 2-tensor” • We want a “truly bimetric theory of gravity” • Different from two copies of GR (we have proven)
Novel Features
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Ø Metrics conformally related.
Ø Now possible to get exact ΛCDM without vacuum energy: o Only B1 and Ωm
0 nonzero:
o Only B2 and Ωm0 nonzero:
o Only B3 and Ωm0 nonzero:
Ø Partially massless gravity:
o Fierz-Pauli mass is fully determined in terms of Λ:
o Potentially dangerous, helicity-zero component of spin-2 field decouples, leaving 4 healthy propagating mode.
o PM treats the 2 metrics on an equal footing and introduces a symmetry between them. The symmetry protects Λ.
o But no viable cosmological solution in Hassan-Rosen theory.
Our doubly coupled bimetric theory results in a natural PM gravity with viable cosmology:
Now viable!
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 12
① A comprehensive statistical analysis of Hassan-Rosen ghost-free, massive, bimetric gravity (for cosmology at background level) + several analytical explanations of results has been done.
② The theory can give “accelerated expansion” with no explicit cosmological constant.
③ The generalization of the theory to a truly (doubly coupled) theory of gravity has been shown to be theoretically viable.
④ It gives exact ΛCDM without vacuum energy (at background level) and a PM theory of gravity.
⑤ Some conceptual issues in this setup need to be addressed: physical metric, equivalence principle.
⑥ Perturbative analysis is needed to further test both theories and break the degeneracies between parameters.
⑦ Local gravitational experiments and astrophysical observations are essential.
Summary, Conclusions and Perspectives +2
Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 13
for your attention