View
32
Download
0
Category
Preview:
DESCRIPTION
f(R) Modified Gravity Cosmological & Solar-System Tests. arXiv:1009.3488. 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. - PowerPoint PPT Presentation
Citation preview
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
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic Expansion Cosmic Structure Solar-System Test
Cosmological Test Local 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 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)
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic Expansion Cosmic Structure Solar-System Test
Cosmological Test Local Test
qj : other cosmological parametersfini : initial condition of f(R)
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
Consider the expansion H(t) parametrized viathe Chevallier-Polarski-Linder weff(z):
zzwwzw aCPL 10
jinia qfwwRf ,,,; 0 construct
f / H
02 +
6
DE
20HR
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic Expansion Cosmic Structure Solar-System Test
Cosmological Test Local Test
qj : other cosmological parametersfini : initial condition of f(R)
Then, proceed to the other two tests of
jinia qfwwRf ,,,; 0“designer f(R)”
OUR APPROACH
Consider the expansion H(t) parametrized viathe Chevallier-Polarski-Linder weff(z):
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)
jinia qfwwRf ,,,; 0 construct
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic Expansion Cosmic Structure Solar-System Test
Cosmological Test Local Test
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
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic Expansion Cosmic Structure Solar-System Test
Cosmological Test Local Test
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
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic Expansion Cosmic Structure Solar-System Test
Cosmological Test Local Test
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
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic Expansion Cosmic Structure Solar-System Test
Cosmological Test Local Test
Rif viable
effwconstant initial
2
2
RRi
RR
R
ffR
ff
R
ff
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic StructureCosmic Expansion Solar-System Test
Cosmological Test Local 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
f(R) Modified Gravity (MG): RfRgxdG
Sg4
16
1
Cosmic StructureCosmic Expansion Solar-System Test
Cosmological Test Local 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 ,
Recommended