2010/09/27 COSMO/CosPA @ Tokyo Univ.

1. f(R) Modified Gravity Cosmological & Solar-System Tests arXiv:1009.3488 Je-An Gu顧哲安 臺灣大學梁次震宇宙學與粒子天文物理學研究中心 Leung Center for Cosmology and Particle Astrophysics (LeCosPA), NTU Collaborators : Wei-Ting Lin林韋廷@ Phys, NTU Dark Energy Working Group @ LeCosPA & NCTS-FGCPA 2010/09/27 COSMO/CosPA @ Tokyo Univ.

2. f(R) Modified Gravity(MG): Explain cosmic acceleration Model (parameterize) deviation from GR Cosmic Structure Cosmic Expansion Solar-System Test Purposes as an essence of cosmology, need to pass as a theory of modified gravity, need to pass Cosmological Test Local Test

3. f(R) Modified Gravity(MG): “designer f(R)” FACT For a given expansion history H(t), one can reconstruct f(R) which generates the required H(t). OUR APPROACH with current observational constraints (WMAP7+BAO+SN): Consider the expansion H(t) parametrized via the Chevallier-Polarski-Linderweff(z): Cosmic Structure Cosmic Expansion  construct Solar-System Test fini : initial condition of f(R) qj : other cosmological parameters Cosmological Test Local Test

4. f(R) Modified Gravity(MG): “designer f(R)” FACT For a given expansion history H(t), one can reconstruct f(R) which generates the required H(t). OUR APPROACH Consider the expansion H(t) parametrized via the Chevallier-Polarski-Linderweff(z): Cosmic Structure Cosmic Expansion  construct Solar-System Test Cosmological Test Local Test Example weff = 1 f/H02 +6DE fini : initial condition of f(R) qj : other cosmological parameters

5. f(R) Modified Gravity(MG): Then, proceed to the other two tests of “designer f(R)” OUR APPROACH with observational constraints (WMAP7+BAO+SN): Consider the expansion H(t) parametrized via the Chevallier-Polarski-Linderweff(z): Cosmic Structure Cosmic Expansion  construct Solar-System Test Cosmological Test Local Test fini : initial condition of f(R) qj : other cosmological parameters

6. f(R) Modified Gravity(MG): Key quantities distinguishing GR & MG defined in : Perturbed metric: Evolution eqn. of matter density perturbation: Cosmic Structure Cosmic Expansion late-time, sub-horizon Solar-System Test Cosmological Test Local Test

7. f(R) Modified Gravity(MG): Cosmological Test Local Test f(R) MG GR late-time, sub-horizon “designer f(R)” Cosmic Structure Cosmic Expansion  function of Solar-System Test

8. f(R) Modified Gravity(MG): Cosmological Test Local Test most f(R) GR Cosmic Structure Cosmic Expansion Solar-System Test E.g. weff = 1 For the present time and k=0.01h/Mpc. / (now) Similar behavior for other weff(z). Observational constraint (Giannantonio et al, 2009):

9. f(R) Modified Gravity(MG): Cosmological Test Local Test Cosmic Structure Cosmic Expansion Solar-System Test

10. f(R) Modified Gravity(MG): Constraint on f(R) MG with Chameleon Mechanism survey around GR point parameter space f = constant  Viable Cosmic Structure Cosmic Expansion closely mimicking GR+ Solar-System Test Cosmological Test Local Test very small viable region indistinguishable from GR !!

11. f(R) Modified Gravity(MG): Cosmological Test Local Test GR fRi Cosmic Structure Cosmic Expansion Solar-System Test Constraint on f(R) MG with Chameleon Mechanism The viable f(R) models in the parameter space (weff,fRi) around the GR point (1,0) for constant weff.

12. Conclusion (observational) Designer w.r.t. the constraint on {w0,wa} (by design) can pass the cosmic-expansion test. The existence of the designer models which pass the cosmic-structure test would require fine-tuning of initial condition fini. Cosmic Structure Cosmic Expansion Solar-System Test Among the designer models, only those closely mimicking GR+ (in all the 3 tests) can pass the solar-system test. As a result, the solar-system test rules out the frequently studied models that are distinct from CDM in .