munich 2008 luca amendola inaf/osservatorio astronomico di roma the dark side of gravity
TRANSCRIPT
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
Munich 2008
Which are the effects of modified gravity atbackground linear level ?non-linear
{ }
Modified gravity
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 !
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…
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 G
L
HH
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)
Munich 2008
Is this already ruled out by
local gravity? matterL+Rfgxd )(4
is a scalar-tensor theory with Brans-Dickeparameter ω=0 or
a coupled dark energy model with coupling β=1/2
''
1
)1()3
41(
2
/2*
fm
eGeGG rrm
α
λAdelberger et al. 2005
Munich 2008
The fourfold way out of local
gravity
)3
41( 2* rmeGG
,m { depend on timedepend on spacedepend on local densitydepend on species
Munich 2008
Sound horizon in R+R Sound horizon in R+R - - nn model model
dec
dec
z
z
s
zH
dz
zH
dzc
0 )(/
)(
2/1ta
L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302, astro-ph/0603173
matterL+R
μRgxd
44
Turner, Carroll, Capozziello etc. 2003
in the Matter Era !
Munich 2008
MG in the background (JF)
321
23
22
1
16
'6
'
'
xxx=ΩH
Rx
Hf
fx
Hf
fx
m
An autonomous dynamical system
f
Rfr
f
Rfrm
'
'
'')(
)2(2]/[
'
)42(]/[
'
31'
3332
313
13232
312
312
1231
xxxxm
xxx
xxxxxm
xxx
xxxxxx
characteristic function
r
prrmeRRf
r
rnrmRRRf
nmRRf
mRRf
qRp
n
n
)()(
1)()(
1)(
0)(
Munich 2008
Classification of f(R) solutions
,...)21
)1(2(
,...)1
3(
)0,5,4(
)0,0,1(
)0,0,1(
)2,1,0(
6
5
4
3
2
1
m
mP
m
mP
P
P
P
P
deSitter acceleration, w = -1
General acceleration, any w0
)1(2
)107(1
0
0
2
0
2
m
m
m
m
m
m
m
mm
For all f(R) theories:
wrong matter era (t1/2)
good matter era (t2/3) for m≥0
Munich 2008
The triangle of viable trajectoriescosmologically viable trajectories
baRRf )()(
pp
p
RRRf 1
1
1 )()(naRRRf )(
Notice that in the triangle m>0
L.A., D. Polarski, S. Tsujikawa 2007 PRD astro-ph/0612180
fRfr
fRfrm
/'
'/'')(
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;....
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
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
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)
Munich 2008
MG at the linear level
scalar-tensor models
2
2
2
2
0,
*
'
')(
'32
)'(2)(
FF
Fa
FF
FF
FG
GaQ
cav
0),(
1),(
ak
akQ
standard gravity
DGP
13
2)(
21;3
11)(
a
wHraQ DEc
f(R)
Ra
km
Ra
km
a
Ra
km
Ra
km
FG
GaQ
cav2
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...)(
...)(
a
aQ
Boisseau et al. 2000Acquaviva et al. 2004Schimd et al. 2004L.A., Kunz &Sapone 2007
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
Munich 2008
Peculiar velocities
xH
xvrz
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
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:
Ha
k
Ha2
'
'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:
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:
Ha
k
Ha2
'
'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:
Munich 2008
The Euclid theorem
From these we can estimate deviations from Einstein’s gravity:
),(),,(),,(),,(),,( zkzkzkzkzkb
),(4 22 akQGak
),( ak
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
Munich 2008
Weak lensing
Weak lensing tomography over half sky
LCDM
DGP
L.A., M. Kunz, D. Sapone arXiv:0704.2421DiPorto & L.A. 2007
ad
d
log
log
Euclid forecast Present constraints
02.0
4.0
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
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
Munich 2008
Weak lensing measures Dark Gravity
scalar-tensor model
Weak lensing tomography over half sky V. Acquaviva, L.A., C. Baccigalupi, in prep.
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...
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. 2004
Dilatonic dark energy: L.A., M. Gasperini, D. Tocchini-Valentini, C. Ungarelli, Phys. Rev. D67, 043512, 2003