2010/09/27 cosmo/cospa @ tokyo univ

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

f(R) Modified Gravity (MG): RfRgxdG

Sg4

16

1

Cosmic Expansion Cosmic Structure Solar-System Test

Cosmological Test Local 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


Sg4

16

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 viathe Chevallier-Polarski-Linder weff(z):

zzwwzw aCPL 10

withcurrent observational constraints (WMAP7+BAO+SN):

72.071.00 41.0,13.093.0

053.0980.0

a

eff

ww

w

(2)

constant (1)

jinia qfwwRf ,,,; 0 construct

qj : other cosmological parametersfini : initial condition of f(R)


Sg4

16

1




Exampleweff = 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


zzwwzw aCPL 10


f / H

02 +

6

DE

20HR


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16

1




Then, proceed to the other two tests of

jinia qfwwRf ,,,; 0“designer f(R)”

OUR APPROACH


zzwwzw aCPL 10

withobservational constraints (WMAP7+BAO+SN):

72.071.00 41.0,13.093.0

053.0980.0

a

eff

ww

w

(2)

constant (1)



Sg4

16

1



Key quantities distinguishing GR & MG

G

Geff

Perturbed metric:

jiij dxdxadtds 2121 222

Evolution eqn. of matter density perturbation:

defined in :

042 mmeffmm GH late-time,sub-horizon


Sg4

16

1



GR

1

1G

Geff

R

RR

R

RR

R

eff

ff

ak

ff

ak

fG

akG

131

141

1

1,

2

2

2

2

R

RR

R

RR

ff

ak

ff

ak

ak

121

141

,

2

2

2

2

f(R) MG

initial ; , 2

2

RRiRRR ffR

ff

R

ff

late-time,sub-horizon

jinia qfwwRf ,,,; 0

“designer f(R)”

;,, ; ; , 0

jRia qfwwRfak function of


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16

1



E.g. weff = 1

For the present timeand k = 0.01h / Mpc.

1Mpc 01.0 hk Rif3210

/

(n

ow

)

403.11 GGeff 996.11

Observational constraint (Giannantonio et al, 2009):

initial

2

2

RRi

RR

R

ffR

ff

R

ff

GR

mostf (R)

Similarbehaviorfor other weff(z).

73.027.0

eff

m


Sg4

16

1



Rif viable

effwconstant initial

2

2

RRi

RR

R

ffR

ff

R

ff


Sg4

16

1

Cosmic StructureCosmic Expansion Solar-System Test


Constraint on

52 0

010 15

RR

R

Rf

f

f(R) MG withChameleon Mechanism

37

10

10

101

Ri

eff

f

w closelymimicking

GR +

parameter space

survey around GR point

f = constant

0 , 1

Viable inieff fwRf ,;

6

6

10 1

10 1

G

Geff

indistinguishable from GR !!

very small viable region


Sg4

16

1

Cosmic StructureCosmic Expansion Solar-System Test


Constraint on

52 0

010 15

RR

R

Rf

f

f(R) MG withChameleon Mechanism

The viable f(R) models in the parameter space (weff, fRi)

around the GR point (1,0) for constant weff.

effw1

f Ri

GR

Conclusion

Cosmic Expansion

Solar-System Test

Cosmic Structure The existence of the designer models which pass the cosmic-structure test would require fine-tuning of initial condition fini.

inia fwwRf ,,; 0

Designer w.r.t. the constraint on {w0,wa} (by design) can pass the cosmic-expansion test.

inia fwwRf ,,; 0

(observational)

Among the designer models, only those closely mimicking GR + (in all the 3 tests) can pass the solar-system test.

inia fwwRf ,,; 0

As a result, the solar-system test rules out

the frequently studied models that are distinct from CDM in .

inifRf ; 1effw

GGeff ,

2010/09/27 cosmo/cospa @ tokyo univ

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