Munich 2008 Luca Amendola INAF/Osservatorio Astronomico di Roma The dark side of gravity.
Luca Amendola INAF/Osservatorio Astronomico di Roma
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Munich 2008Luca Amendola
INAF/Osservatorio Astronomico di Roma
The dark side ofgravity
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Munich 2008
Why DE/MG is interesting
How to observe it
g
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Munich 2008
Observations are converging…
…to an unexpected universe
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Munich 2008
Classifying the unknown
a) change the equations i.e. add new matter field (DE) or modify gravity (MG)b) change the metrici.e. inhomogeneous non-linear effects, void models, etc
Standard cosmology:GR gravitational equations + FRW metric
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Munich 2008
Which are the effects of modified gravity atbackground linear level ?non-linear
{ }
Modified gravity
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Munich 2008
Cosmology and modified gravity
in laboratory
in the solar system
at astrophysical scales
at cosmological scales
} very limited time/space/energy scales;only baryons
complicated by non-linear/non-gravitational effects
unlimited scales; mostly linear processes;baryons, dark matter, dark energy !
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Munich 2008
How to hide modified gravity (in the solar system)
L.A., C. Charmousis, S. Davis, PRD 2008, arXiv 0801.4339
Generalized Brans-Dicke-Gauss-Bonnet Lagrangian
Solution in static spherical symmetry in a linearizedPPN metric with
1/U
Conclusion: there are solutions which look “Einsteinian” but are not…
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Munich 2008
L = crossover scale:
• 5D gravity dominates at low energy/late times/large scales• 4D gravity recovered at high energy/early times/small scales
5D Minkowski bulk:
infinite volume extra dimension
gravity leakage
2
1
1
rVLr
rVLr
brane
Simplest MG (I): DGP
RgxdLRgxdS 4)5()5(5
(Dvali, Gabadadze, Porrati 2000)(Dvali, Gabadadze, Porrati 2000)
3
82 GLHH
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Munich 2008
f(R) models are simple and self-contained (no need of potentials) easy to produce acceleration (first inflationary model) high-energy corrections to gravity likely to introduce higher-order terms particular case of scalar-tensor and extra-dimensional theory
matterL+Rfgxd 4eg higher order corrections ...324 RR+Rgxd
The simplest MG in 4D: f(R)
Simplest MG (II): f(R)
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Munich 2008
Is this already ruled out by local gravity?
matterL+Rfgxd )(4is a scalar-tensor theory with Brans-Dicke
parameter ω=0 or a coupled dark energy model with coupling β=1/2
''1
)1()341(
2
/2*
fm
eGeGG rrm
α
λAdelberger et al. 2005
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Munich 2008
The fourfold way out of local gravity
)341( 2* rmeGG
,m { depend on timedepend on spacedepend on local densitydepend on species
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Munich 2008
Sound horizon in R+R Sound horizon in R+R - - nn model model
dec
dec
z
z
s
zHdz
zHdzc
0 )(/
)(
2/1ta
L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302, astro-ph/0603173
matterL+RμRgxd
44
Turner, Carroll, Capozziello etc. 2003
in the Matter Era !
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Munich 2008
A recipe to modify gravity
Can we find f(R) models that work?
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Munich 2008
MG in the background (JF)
321
23
22
1
16
'6
''
xxx=ΩHRx
Hffx
Hffx
m
An autonomous dynamical system
fRfr
fRfrm
'''')(
)2(2]/[
'
)42(]/[
'
31'
3332
313
13232
312
312
1231
xxxxm
xxx
xxxxxm
xxx
xxxxxx
characteristic function
rprrmeRRf
rrnrmRRRf
nmRRf
mRRf
qRp
n
n
)()(
1)()(
1)(
0)(
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Munich 2008
MG in the background
ΩKΩP
Ωγ
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Munich 2008
Classification of f(R) solutions
,...)21
)1(2(
,...)13(
)0,5,4()0,0,1(
)0,0,1()2,1,0(
6
5
4
3
2
1
mmP
mmP
PPPP
deSitter acceleration, w = -1
General acceleration, any w0
)1(2)107(1
0020
2
m
m
m
m
m
m
mmm
For all f(R) theories:
wrong matter era (t1/2)
good matter era (t2/3) for m≥0
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Munich 2008
The power of the m(r) method
REJECTED
REJECTED
REJECTED
REJECTED
1/0)( ReRRf
REJECTED
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Munich 2008
The triangle of viable trajectoriescosmologically viable trajectories
baRRf )()(
ppp
RRRf 11
1 )()(naRRRf )(
Notice that in the triangle m>0L.A., D. Polarski, S. Tsujikawa 2007 PRD astro-ph/0612180
fRfrfRfrm
/''/'')(
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Munich 2008
Local Gravity Constraints are very tight
Depending on the local field configuration
623 1010'
'')( s
sss f
fRRm
depending on the experiment: laboratory, solar system, galaxy
see eg. Nojiri & Odintsov 2003; Brookfield et al. 2006Navarro & Van Acoyelen 2006; Faraoni 2006; Bean et al. 2006;Chiba et al. 2006; Hu, Sawicky 2007; Mota et al. 2006;....
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Munich 2008
cLGC+Cosmology
Take for instance the ΛCDM clone
baRRf )()(
Applying the criteria of LGC and background cosmology
23101 ba
i.e. ΛCDM to an incredible precision
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Munich 2008
What background hidesperturbations reveal
The background expansion only probes H(z)
The (linear) perturbations probe first-order quantities
Full metric reconstruction at first order requires 3 functions
)])(21()21[( 222222 dzdydxdtads
),(),()( zkzkzH
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Munich 2008
Two free functions
At the linear perturbation level and sub-horizon scales, a modified gravity model will
mmakQGak ),(4 22 modify Poisson’s equation
induce an anisotropic stress
)])(21()21[( 222222 dzdydxdtads
),( ak
(most of what follows in collaboration with M. Kunz, D. Sapone)
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Munich 2008
MG at the linear level
scalar-tensor models
2
2
2
2
0,
*
'')(
'32)'(2)(
FFFa
FFFF
FGGaQcav
0),(1),(
akakQ
standard gravity
DGP
132)(
21;311)(
a
wHraQ DEc
f(R)
Rakm
Rakm
a
Rakm
Rakm
FGGaQcav
2
2
2
2
2
2
2
2
0,
*
21)(,
31
41)(
Lue et al. 2004; Koyama et al. 2006
Bean et al. 2006Hu et al. 2006Tsujikawa 2007
coupled Gauss-Bonnet see L. A., C. Charmousis, S. Davis 2006...)(
...)(
aaQ
Boisseau et al. 2000Acquaviva et al. 2004Schimd et al. 2004L.A., Kunz &Sapone 2007
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Munich 2008
Reconstruction of the metric
b
zkbzkPgal
'
),()1(),,( 2222
2)(),( zkPellipt
Correlation of galaxy positions:galaxy clustering
Correlation of galaxy ellipticities:galaxy weak lensing
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Munich 2008
Peculiar velocities
xHxv
rz
0
rz PP )1( 2
b '
Correlation of galaxy velocities:galaxy peculiar field
Guzzo et al. 2008
redshift distortion parameter
rz PP )1( 2
=0.70±0.2
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Munich 2008
The Euclid theorem
1),,(/),,('),,(
transvzkPradzkPb
transvzkPb
2
0
)()'('),( z
ellipt zKdzzkP
We can measure 3 combinations and we have 2 theoretical relations…
),(),,(),,(),,(),,( zkzkzkzkzkb
Observables: Conservation equations:
HakHa
2
'
'3'
Theorem: lensing+galaxy clustering allows to measure all (total matter) perturbation variables at first order without
assuming any particular gravity theory
5 unknown variables:
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Munich 2008
The Euclid theorem
1),,(/),,('),,(
transvzkPradzkPb
transvzkPb
2
0
)()'('),( z
ellipt zKdzzkP
We can measure 3 combinations and we have 2 theoretical relations…
),(),,(),,(),,(),,( zkzkzkzkzkb
Observables: Conservation equations:
HakHa
2
'
'3'
Theorem: lensing+galaxy clustering allows to measure all (total matter) perturbation variables at first order without
assuming any particular gravity theory
5 unknown variables:
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Munich 2008
The Euclid theorem
From these we can estimate deviations from Einstein’s gravity:
),(),,(),,(),,(),,( zkzkzkzkzkb
),(4 22 akQGak
),( ak
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Munich 2008
EuclidA geometrical probe of the universe proposed for Cosmic Vision
= +
All-sky optical imaging for gravitational lensing
All-sky near-IR spectra to H=22 for BAO
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Munich 2008
Weak lensing
Weak lensing tomography over half sky
LCDM
DGP
L.A., M. Kunz, D. Sapone arXiv:0704.2421DiPorto & L.A. 2007
add
loglog
Euclid forecast Present constraints
02.0
4.0
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Munich 2008
Power spectrum
Galaxy clustering at 0<z<2 over half sky ....if you know the bias to 1%
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Munich 2008
Non-linearity in BAO
Matarrese & Pietroni 2007
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Munich 2008
Poster advertisement
See poster by Miguel Quartin…
Quercellini, Quartin & LA, arXiv 0809.3675
yrst 10
as 11.0
LTB void model
Garcia-Bellido & Haugbolle 2008
Cosmic parallax
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Munich 2008
Conclusions
Two solutions to the DE mismatch: either add “dark energy” or “dark gravity” High-precision next generation cosmological observations are the best tool to test for modifications of gravity It is crucial to combine background and perturbations A full reconstruction to first order requires imaging and spectroscopy: Euclid
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Munich 2008
Luca AmendolaINAF/Osservatorio
Astronomico di Roma
The bright side ofMunich
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Munich 2008
Weak lensing measures Dark Gravity
scalar-tensor model
Weak lensing tomography over half sky V. Acquaviva, L.A., C. Baccigalupi, in prep.
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Munich 2008
Non-linearity in WL
Weak lensing tomography over half sky
=1000,3000,10000
log
max
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Munich 2008
Non-linearity in BAO
Matarrese & Pietroni 2007
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Munich 2008
Conclusions: the teachings of DE
Two solutions to the DE mismatch: either add “dark energy” or “dark gravity”The high precision data of present and near-future observations allow to test for dark energy/gravityNew MG parameters: γ,Σ A general reconstruction of the first order metric requires galaxy correlation and galaxy shear Let EUCLID fly...
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Munich 2008
References
Basics: L.A. , Phys. Rev. D62, 043511, 2000; L.A. , Phys. Rev. D62, 043511, 2000;CMB: L.A. , Phys. Rev. Lett. 86,196,2001; L.A. , Phys. Rev. Lett. 86,196,2001;Bias: L.A. & D. Tocchini-Valentini, PRD66, 043528, L.A. & D. Tocchini-Valentini, PRD66, 043528,
20022002WMAP: astro-ph/0303228, Phys Rev 2003 astro-ph/0303228, Phys Rev 2003N-body: : A. Maccio’ et al. 2004A. Maccio’ et al. 2004Dilatonic dark energy: L.A., M. Gasperini, D. Tocchini-
Valentini, C. Ungarelli, Phys. Rev. D67, 043512, 2003
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Munich 2008
Current Observational Status: CFHTLS
First resultsFrom CFHT Legacy Survey with Megacam
(w=constant and other priors assumed)
Weak Lensing
Type IaSuper-novae
Hoekstra et al. 2005Semboloni et al. 2005
Astier et al. 2005