1. Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. ， Bassett, Nichol, Suto, Yahata, (PRD 2006) K.Y. ， Parkinson, Hamana, Nichol, Suto, (PRD 2007) Discussion by HSC Weak Lensing Working Group

2. INTRODUCTION Modified Gravity models as alternative to the dark energy f(R) gravity model, TeVeS theory, DGP model, etc. ・・・ ambitious challenges to the fundamental physics necessary step to go beyond the standard model ? All these models may not be complete, but are A lot of observational projects of the dark energy are proposed, These results might be useful to test modified gravity theory. WFMOS, HSC, DES, DUNE, LSST, JDEM, BOSS, ・・・ Future feasibility of testing gravity models ? Optimized strategy of future survey of HSC ? 2

3. Investigation of the observational consequences of typical model is thought-provoking, because we can learn what can be possible signatures of such generalized gravity models. The DGP model as an example (Dvali, Gabadadze, Porrati, 00) Brane world scenario, (3+1)-dim brane in (4+1)-dim. bulk It is possible to construct a self-accelerating universe, without introducing dark energy, by choosing a scale parameter, r c =M 4 2 /2M 5 2, defined by the ratio of the Planck scales, properly. (Deffayet, 01) Modified Friedmann equation (flat universe) Modification of expansion history changes the distance redshift relation ３

4. can be tested using SNe, BAO, CMB Modified relation of the background expansion, distance-redshift relation (K.Y., Bassett, Nichol, Suto, Yahata) (e.g., Maartens, Majerroto 06) Constraint using Baryon Oscillation 4 dlnP(k)/dlnk The Λ - model and the DGP model the same cosmological parameter and the same data analysis, Area 2000 deg 2 n = 5×10 -4 (h -1 Mpc) -3 0.5 ＜ z ＜ 1.3 WFMOS-like sample One can distinguish between the Lambda model and the DGP model clearly difference of H(z) and r(z), the peaks shift.

5. The background expansion is parameterized in general (flat universe) The expansion history of the DGP model is reproduced by the dark energy model of the equation of state Ω m ～ 0.3 The expansion history of M.G. can be described equivalently by the parameterization of the dark energy model. (Linder, 04) 5

6. Perturbation is important as an independent information (Maartens, Koyama 06)Perturbation of the cosmological DGP model Evolution of Growth factor Modified Poisson equation Anisotropic stress (sub-horizon sclale) 6

7. Evolution of Growth factor ΛCDM DGP Dark Energy Same expansion H(z) growth factor is important to distinguish between the gravity models. 7

8. Phenomenological description of the perturbation for generalized gravity models (Amin, Wagoner, Blandford 07; Jain, Zhang 07; Hu, Sawicki 07; Caldwell, Cooray, Melchiotti 07…) (Amendola, Kunz, Sapone 07) General relativity Generalized model 8

9. Parameterization of the growth factor (Lahav 91, Wang, Steinhardt 98, Percival 05, Linder 05) γ characterizes the modification of gravity the dark energy model in general relativity the DGP model The difference of the growth of density perturbation is described by γ. Other way of description of modified gravity 9 The fitting formula works

10. ΛCDM DGPDark Energy γ ＝ 0.56 γ ＝ 0.68 Parameterization by γ reproduces the evolution Evolution of growth factor 10

11. Observational constraints on γ Porto & Amendola (07) Nesseris & Perivolaropoulos (07) Lyman-α forest clustering Galaxy clustering and redshift space distortion Measurement of γ 11

12. Importance of measuring γ as a consistency test of the growth of density perturbation and gravity model The weak shear is useful to measure the evolution of the density perturbation, and to test modified gravity models ( Ishak, Upadhye, Spergel 06; Huteter, Linder 07; Amendola, Kunz, Sapone 07; Jain, Zhang 07 Heavens, Kitching, Verde 07; etc…) Weak shear power spectrum Number count per unit solid angle 12

13. Feasibility of measuring γ with the HSC Weak Lens survey? Fisher Matrix Analysis Growth of density perturbation Background expansion Analysis in the 7 parameters space γ marginalized flat universe, Assumption; 13

14. Amara & Refregier (06) arcmin -2 (SNAP simulation) (number density arcmin -2 ) (mean redshift) exposure time Modeling of Galaxy distribution / 1 Field of View / 1 passband filter The Validity of this relation for the HSC is now investigated by WLWG. 14

15. Total observation time = 100 nights (fixed) Field of view = 1.5 degree Overheard time = 10% of exposure time + operation time (t operation =5 minutes) (one band exposure time for one FoV) Total survey area Assumption of the HSC WL survey 15

16. Total survey area=1700 deg. 2 t exp =10mins./1FoV/passband Total survey area as a function of t exp Total observation time = 100 nights 4 passband filters 16

17. 1σ error as a function of t exp Constraint on γ from the WL shear power spectrum photo-z error only used the sample The observation of 100 nights will be difficult to achieve 17 Marginalized Fisher matrix

18. Constraint on γ from the WL shear power spectrum + galaxy power spectrum (BAO) from WFMOS like spectroscopy survey 1σ error as a function of t exp Assumed additional spectroscopy survey of the same survey area as the WL survey of the number density in the redshift range Combination with the WFMOS improves the constraint WL + BAO 18

19. Summary & Conclusion Dark energy survey is useful to test modified gravity models Simple consistency test is to measure γ parameter The weak lensing method is useful to constrain γ The HSC alone would not provide a strong constraint, but the combination with the WFMOS improve it, and Δ γ ≦ 0.07 might be possible. (2σ level for differentiating between the DE and the DGP) Slightly depends on the modeling of the galaxy count, dN/dz Synergy with the cluster count ? finding the optimized survey strategy of HSC 19 HSC Weak Lens Working Group is investigating it