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