Cosmology of Ghost-free Bimetric Gravity:

Late-time Acceleration and Double-coupling Generalization

COSMO 2013 / Cambridge / September 5, 2013

Yashar Akrami Postdoctoral Fellow Institute of Theoretical Astrophysics University of Oslo, Norway

with: Tomi S. Koivisto, David F. Mota & Marit Sandstad

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 +2

Demand for Massive Gravity A natural IR-modification of gravity: give mass to gravitons Fierz & Pauli (1939):

(linearized metric fluctuations around flat space-time)

The only ghost-free mass term:

Consistent Non-linear Completion? Theoretically challenging, cosmologically interesting. 2011: breakthrough

de Rham & Gabadadze [arXiv:1007.0443] de Rham, Gabadadze & Tolley [arXiv:1011.1232] • The only ghost-free, massive gravity Hassan & Rosen [arXiv:1103.6055] [arXiv:1106.3344] • The only ghost-free, [arXiv:1109.3515] bimetric gravity [arXiv:1111.2070] Hassan, Rosen & Schmidt-May [arXiv:1109.3230]

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 2 +2

Bimetric Theory of Gravity

Hassan-Rosen bimetric gravity based on de-Rham-Gabadadze-Tolley massive gravity:

Action:

• 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 +2

Isotropic and Homogeneous Universe

Metrics:

Evolution:

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 4 +2

Observational Constraints

Model Parameter: B , B , B , B , B Ω 0 0 1 2 3 4, m

(no Ωϒ, no curvature)

(B0=0) Data: (purely background) 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

DL, DV, DA, H(z) Scanning Method: State-of-the-art scanning algorithm: MultiNest (nested sampling): MCMC-like (both Bayesian and frequentist statistics)

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 5 +2 0 Only B1 and Ωm nonzero

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 6 +2 0 Only B1 and Ωm nonzero

Graviton Mass: 2 2 2 m = 1.45 H0 ± 0.25 H0

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 7 +2 0 Only B1 and Ωm nonzero

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 8 +2 0 Only B1 and Ωm nonzero

ΩΛ = B1y

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 9 +2

Full Results

• 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 +2

Generalization: doubly coupled bigravity

• 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)

Action

Shown to be theoretically consistent Dust-dominated universe:

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 11 +2

Novel Features

Ø Metrics conformally related. Ø Now possible to get exact ΛCDM without vacuum energy: 0 o Only B1 and Ωm nonzero:

0 o Only B2 and Ωm nonzero: Now viable! 0 o Only B3 and Ωm 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:

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 12 +2 Summary, Conclusions and Perspectives

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.

Yashar Akrami / Institute of Theoretical Astrophysics, University of Oslo / Cambridge, September 5, 2013 13 for your attention