1. 2010/09/27 COSMO/CosPA @ Tokyo Univ. f(R) Modified Gravity Cosmological & Solar-System Tests 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 arXiv:1009.3488

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

3. f(R) Modified Gravity (MG): Cosmic ExpansionCosmic StructureSolar-System Test Cosmological TestLocal Test For a given expansion history H(t), one can reconstruct f(R) which generates the required H(t). FACT “designer f(R)” OUR APPROACH Consider the expansion H(t) parametrized via the Chevallier-Polarski-Linder w eff (z): with current observational constraints (WMAP7+BAO+SN):  construct q j : other cosmological parametersf ini : initial condition of f(R)

4. f(R) Modified Gravity (MG): Cosmic ExpansionCosmic StructureSolar-System Test Cosmological TestLocal Test q j : other cosmological parametersf ini : initial condition of f(R) Example w eff =  1 For a given expansion history H(t), one can reconstruct f(R) which generates the required H(t). FACT “designer f(R)” OUR APPROACH Consider the expansion H(t) parametrized via the Chevallier-Polarski-Linder w eff (z):  construct f / H 0 2 + 6  DE

5. f(R) Modified Gravity (MG): Cosmic ExpansionCosmic StructureSolar-System Test Cosmological TestLocal Test q j : other cosmological parametersf ini : initial condition of f(R) Then, proceed to the other two tests of “designer f(R)” OUR APPROACH Consider the expansion H(t) parametrized via the Chevallier-Polarski-Linder w eff (z): with observational constraints (WMAP7+BAO+SN):  construct

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

7. f(R) Modified Gravity (MG): Cosmic ExpansionCosmic StructureSolar-System Test Cosmological TestLocal Test GR f(R) MG late-time, sub-horizon “designer f(R)”  function of

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

9. f(R) Modified Gravity (MG): Cosmic ExpansionCosmic StructureSolar-System Test Cosmological TestLocal Test

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

11. f(R) Modified Gravity (MG): Cosmic StructureCosmic ExpansionSolar-System Test Cosmological TestLocal Test  Constraint on f(R) MG with Chameleon Mechanism The viable f(R) models in the parameter space (w eff, f Ri ) around the GR point (  1,0) for constant w eff. f Ri GR

12. Conclusion Cosmic ExpansionSolar-System TestCosmic Structure  The existence of the designer models which pass the cosmic-structure test would require fine-tuning of initial condition f ini.  Designer w.r.t. the constraint on {w 0,w a } (by design) can pass the cosmic-expansion test. (observational)  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.