Observational test of modified gravity models with future imaging surveys

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

2. 2 INTRODUCTION Modified Gravity models as alternative to the dark energy f(R) gravity model, TeVeS theory, DGP model, etc.・・・ All these models may not be complete, but are ambitious challenges to the fundamental physics necessary step to go beyond the standard model ? 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 ?

3. 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 (Deffayet, 01) It is possible to construct a self-accelerating universe, without introducing dark energy, by choosing a scale parameter, rc=M42/2M52, defined by the ratio of the Planck scales, properly. Modified Friedmann equation (flat universe) Modification of expansion history changes the distance redshift relation

4. 4 Modified relation of the background expansion, distance-redshift relation can be tested using SNe, BAO, CMB (e.g., Maartens, Majerroto 06) Constraint using Baryon Oscillation (K.Y., Bassett, Nichol, Suto, Yahata) The Λ-model andthe DGP model the same cosmologicalparameter and the same data analysis, dlnP(k)/dlnk difference of H(z) and r(z), the peaks shift. WFMOS-like sample Area 2000 deg2 n = 5×10-4 (h-1Mpc)-3 0.5＜z＜1.3 One can distinguish between the Lambda model and the DGP model clearly

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

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

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

8. 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) Generalized model General relativity

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

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

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

12. 12 Importance of measuring γas 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

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

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

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

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

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

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

19. 19 Summary & Conclusion Dark energy survey is useful to test modified gravity models Simple consistency test is to measure γparameter 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 Δγ≦0.07might be possible. (2σlevel for differentiating between the DE and the DGP) Slightly depends on the modeling of the galaxy count, dN/dz HSC Weak Lens Working Group is investigating it Synergy with the cluster count ? finding the optimized survey strategy of HSC