![Page 1: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/1.jpg)
Observational test of modified gravity modelswith 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
![Page 2: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/2.jpg)
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
![Page 3: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/3.jpg)
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, rc=M4
2/2M52,
defined by the ratio of the Planck scales, properly.
(Deffayet, 01)
Modified Friedmann equation (flat universe)
mc
2 ρ3
8π=
r
H-H
G
Modification of expansion history changes the distance redshift relation
z
zH
dzz
0 )'(
')(
3
![Page 4: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/4.jpg)
can be tested using SNe, BAO, CMBModified 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 deg2
n = 5×10-4 (h-1Mpc)-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.
![Page 5: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/5.jpg)
The background expansion is parameterized in general (flat universe)
z1
z3w)ww3(1
m3m2
02 ez))(1Ω-(1
z)(1Ω
HH(z) 0a
a
The expansion history of the DGP model is reproduced by the dark energy model of the equation of state
z1z
0.32-0.78w(z)
Ωm ~ 0.3
The expansion history of M.G. can be described equivalently by the parameterization of the dark energy model.
z1z
www(z) 0 a
(Linder, 04)
5
![Page 6: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/6.jpg)
Perturbation is important as an independent information
(Maartens, Koyama 06)Perturbation of the cosmological DGP model
)sin(21)(21 22222222 dddtadtds
022
2
2
2
a
k
dt
dH
dt
d
mGak
3
114 22
maG
k 22
3
8
23121
HHHrc
mGak 22 8
Evolution of Growth factor
Modified Poisson equation
Anisotropic stress
(sub-horizon sclale)
6
![Page 7: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/7.jpg)
Evolution of Growth factor
ΛCDM
DGP Dark Energy
Same expansion H(z)
a
aD )(1
a
growth factor is important to distinguish between the gravity models.
7
![Page 8: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/8.jpg)
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)
δρm
22 a4π=Φk
0=Φ+Ψ
G
General relativity
δm
22 ρaQ4πΦk
ηΦΦΨ
G
Generalized model
1Q
0η
)sin()(21)(21 22222222 ddfdtadtds K
0 Ψak
dtdδ
2Hdt
δd2
2
2
2
0δρη)Q(14dtdδ
2Hdt
δd2
2
G
8
![Page 9: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/9.jpg)
Parameterization of the growth factor
a
m aa
da
a
aD0
1 1-)'('
'exp
)(
2
30
20
m aH
aΩH=aΩ
)()(
-
(Lahav 91, Wang, Steinhardt 98, Percival 05, Linder 05)
680=γ .
γ characterizes the modification of gravity
the dark energy model in general relativity
the DGP model
56.0~55.0_
))1(1(05.055.0
zwγ
The difference of the growth of density perturbation is described by γ.
Other way of description of modified gravity9
The fitting formula works
![Page 10: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/10.jpg)
ΛCDM
DGP Dark Energy γ = 0.56γ = 0.68
Parameterization by γ reproduces the evolution
Evolution of growth factor
10
![Page 11: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/11.jpg)
Observational constraints on γ
20.017.067.0
4.03.06.0
Porto & Amendola (07)
Nesseris & Perivolaropoulos (07)
3.02.00.0
a
0 m1 1-)(a'Ω
a'da'
expa(a)D η)(1γ
Lyman-α forest clustering
Galaxy clustering and redshift space distortion
Measurement of γ 11
![Page 12: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/12.jpg)
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…)
)( )(,)(
))(())(()()( χzχl→knonlineaer
22
20
20
jiij massP
a2
ΩH3χzWχzWχd=lP ∫
)'(
(z)-)'(
'
)'('
1)(
1
, ]max[ z
z
dz
zdNdz
NzW
i
i
z
zzi
i
Weak shear power spectrum
')'(
'dz
zdNdz=N
1+i
i
z
zj ∫
dz
zdN )(Number count per unit solid angle
mGak 22 8
12
![Page 13: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/13.jpg)
Feasibility of measuring γ with the HSC Weak Lens survey?
Fisher Matrix Analysis
a
0 m1 1-)(a'Ω
a'da'
expa(a)D γGrowth of density perturbation
Background expansion
1)-(a3w)ww-3(1m
-3m
20
2 e)aΩ-(1aΩHH(a) 0 aa
a)-(1www(a) 0 a
Analysis in the 7 parameters space
sma nhww ,,,,, 80 γ
marginalized
flat universe, Assumption;
13
![Page 14: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/14.jpg)
β0
0
)(z/z-α1)/β)+Γ((αz
βg ezN=
dz
dN(z)1+α
3=β50=α ,.
dz
dNdzz
N
1=z ∫
gm
dz
dNdz=N ∫g
)/( 38Γ
z=z m
0
067.0
.min30exp9.0t
meanz
( )440
30
t
g 30=N.
.minexp
Amara & Refregier (06)
arcmin-2
(SNAP simulation)
(number density arcmin-2)
(mean redshift)
expt 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
![Page 15: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/15.jpg)
operationtnt
1.1
n timeobservatio Total
passbandnumberexp
2
2ViewofFieldArea
Total observation time = 100 nights (fixed)
Field of view = 1.5 degree
Overheard time = 10% of exposure time + operation time (toperation=5 minutes)
expt (one band exposure time for one FoV)
Total survey area
Assumption of the HSC WL survey
4passbandnumber n
15
![Page 16: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/16.jpg)
Total survey area=1700 deg.2 texp=10mins./1FoV/passband
Total survey area as a function of texp
Total observation time = 100 nights4 passband filters
16
![Page 17: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/17.jpg)
1σ error as a function of texp
Constraint on γ from the WL shear power spectrum
photo-z error
)1(05.0 zz
5.105.0 z only used the sample
The observation of 100 nights will be difficult to achieve
1.0
17
Marginalized Fisher matrix
![Page 18: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/18.jpg)
Constraint on γ from the WL shear power spectrum + galaxy power spectrum (BAO) from WFMOS like spectroscopy survey
1σ error as a function of texp
34 Mpch10×4=n ]/[-
4.18.0 z
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 07.0
WL + BAO
18
![Page 19: Observational test of modified gravity models with future imaging surveys Kazuhiro Yamamoto (Hiroshima U.) Edinburgh Oct. 24-26 K.Y. , Bassett, Nichol,](https://reader035.vdocuments.site/reader035/viewer/2022062719/56649edc5503460f94bed7e3/html5/thumbnails/19.jpg)
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 Δγ≦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