Gleevec vs. BMS-354825 Druker vs. Sawyers Yashar Kalani Biochemistry 230.
Yashar Akrami
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Transcript of Yashar Akrami
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Yashar AkramiModern Cosmology: Early Universe, CMB and LSS/ Benasque/ August 17,
2012
Postdoctoral FellowInstitute of Theoretical AstrophysicsUniversity of Oslo, Norway(Hans Kristian Eriksen, David Mota)
with:Tomi S. Koivisto & Marit Sandstad
[arXiv:1208.xxxx]
Cosmic Accelerationfrom
Ghost-free, Massive BiGravity:
A Statistical Analysis with Improved Generality
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Late-time Acceleration
Motivation
2011 Nobel Prize in Physics
“…for the discovery of the accelerating expansion of the Universe through observations of distant supernovae”
Saul Perlmutter Brian P. Schmidt Adam G. Riess
+1
too big:CC problem
=0- Symmetry- Degravitation,- …
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Motivation+1
Dark Energyor
Modified GravityExample: Scalar Fields:
[Luca’s talk]
The most general 4D scalar field theory with second order equation of motion:
Horndeski LagrangianAnyAlternatives?
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Fierz & Pauli (1939):
Demand for Massive Gravity+1
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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:
breakthroughde 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
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Action:
Theory(general)
Hassan-Rosen bimetric gravity based on de-Rham-Gabadadze-Tolley massive gravity:
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Equations of Motion:
Theory(general)
Bianchi Identities + Energy-Momentum Conservation :
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Metrics:
Theory(the case for an isotropic and homogeneous universe)
Bianchi Identities + Energy-Momentum Conservation:
+1
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Generalized Friedmann Equations:
Theory(the case for an isotropic and homogeneous universe)
+1
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Theory(the case for an isotropic and homogeneous universe)
Evolution Equation:
Hubble Parameter:
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Initial Conditions:
one-dimensional phase space
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Observational Constraints:
Scanning Method:
Model Parameter: B0, B1, B2, B3, B4, Ωm
0
(no Ωϒ, no curvature)
(B0=0)
State-of-the-art scanning algorithm: MultiNest (nested sampling): MCMC-like (both Bayesian and frequentist statistics)
+1
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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)
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Some Results:
Minimal Non-linear Extension of Massive Fierz-Pauli Action without CC:
B1, Ωm0:
Best-fit χ2: 551.6P-value: 0.8355Log-Evidence: -281.73
Best-fit χ2: 546.54P-value: 0.8709Log-Evidence: -278.50
ΛCDM:
both consistent with the data (less than 1σ deviation)
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Some Results: (B1, Ωm0)
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Independent of Priors
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Some Results: (B1, Ωm0)
Graviton Mass:m2 = 1.45 H0
2 ± 0.25 H02
Independent of Priors
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Some Results: (B1, Ωm0)
+1
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Some Results: (B1, Ωm0)
+1
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ΩΛ = B1y
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Some Results:
B2, Ωm0
Best-fit χ2: 894.0P-value: < 0.0001Log-Evidence: -450.25
considered to be extremely statistically significant
Excluded!
B3, Ωm0
Best-fit χ2: 1700.5P-value: < 0.0001Log-Evidence: -850.26
+1
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Some Results:
B1, B2, Ωm0
Best-fit χ2: 546.52P-value: 0.8646Log-Evidence: -279.77
consistent with the data within 1σ
B1, B3, Ωm0
Best-fit χ2: 542.82P-value: 0.8878Log-Evidence: -280.10
B2, B3, Ωm0
Best-fit χ2: 548.04P-value: 0.8543Log-Evidence: -280.91
+1
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{-281.73 for (B1, Ωm) & -278.50 for ΛCDM}
{0.8355 for (B1, Ωm) & 0.8709 for ΛCDM}
complexity of the model increases considerably when we increase the number of model parameters
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Some Results: (B1, B2, Ωm0)
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Enlargedprior ranges:
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Some Results: (B1, B2, Ωm0)
+1
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Enlargedprior ranges:
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Some Results: (B1, B2, Ωm0)
+1
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Enlargedprior ranges:
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Some Results: (B1, B2, Ωm0)
+1
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Enlargedprior ranges:
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Some Results: (B1, B2, Ωm0)
+1
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① A comprehensive statistical analysis of Hassan-Rosen ghost-free, massive, bimetric gravity (for cosmology at background level) + several analytical explanations of results,
② Massive gravity can give “Accelerated Expansion” with no explicit Cosmological Constant,
③ Very good fit even in the 1-parameter case,④ Parameters are correlated for the full model,⑤ Background data are not enough to constrain the full
model (not robust and prior-independent),⑥ Analysis of perturbations and other astrophysical
probes needed to break degeneracy and constrain the model,
⑦ Further theoretical generalizations, e.g. curvature, coupling of “f” to matter, other background metrics, etc.
Summary & Conclusions+1
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for your attention