luca amendola inaf/osservatorio astronomico di roma
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SAIT 2008
Luca Amendola
INAF/Osservatorio Astronomico di Roma
The dark side ofgravity
SAIT 2008
Why DE is interesting
How to observe it
g
SAIT 2008
Observations are converging…
…to an unexpected universe
SAIT 2008
GTRgR 82
1
gravity matter
1tot 3.0cluster
Solution: modify either the Matter sector
or the Gravity sector
)( gF )(8 GT
DE
MG
The dark energy problem
SAIT 2008
Can we detect traces of modified gravity atbackground linear level ?non-linear
{ }
Modified gravityModified gravity
SAIT 2008
What is gravity ?
A universal force in 4D mediated by a massless tensor field
What is modified gravity ?
What is modified gravity ?
A non-universal force in nD mediated by (possibly massive) tensor, vector and scalar fields
What is modified gravity?
SAIT 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 !
Cosmology and modified gravity
SAIT 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
RgxdLRgxdS 4)5()5(5
(Dvali, Gabadadze, Porrati 2000)(Dvali, Gabadadze, Porrati 2000)
3
82 G
L
HH
Simplest MG (I) : DGP
SAIT 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 modification of Einstein’s gravity: f(R)
Simplest MG (II): f(R)Simplest MG (II): f(R)
SAIT 2008
Is this already ruled out by local gravity?
''
1
'
4'
''
1
)1()3
41(
22
/2*
ff
fRf
fm
eGeGG rrm
(on a local minimum)
α
λ
Is MG already ruled out by local gravity ?
Yukawa correction to Newton’s potential
SAIT 2008
From dark energy to dark forceFrom dark energy to dark force
rad mat
field
rad mat
fieldMDE
toda
y
9/1=Ωφ
2/1=β
a= t 1/2
)( 3
8
2
33
2
3)'(3
2
m
mmm
m
H
H
VH
2/3t=ainstead of !!
In Jordan frame:
From Dark Energy to Dark Force
L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302, astro-ph/0603173
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A recipe to modify gravity
Can we find f(R) models that work?
A recipe for modified gravity
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The m,r plane
The dynamics becomes 1-dimensional !
The qualitative behavior of any f(R) model can beunderstood by looking at the geometrical properties of the
m,r plot
m(r) curve
crit. line
acceleration
matter era
deSitter
L.A., D. Polarski, S. Tsujikawa, PRD, astro-ph/0612180
f
Rfr
f
Rfrm
'
'
'')(
The m,r plane
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The power of the m(r) method
REJECTED
REJECTED
REJECTED
REJECTED
1/0)( ReRRf
REJECTED
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The triangle of viable trajectories
There exist only two kinds of cosmologically viable trajectories
baRRf )()(
pp
p
RRRf 1
1
1 )()(naRRRf )(
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A theorem on phantom crossing
Theorem: for all viable f(R) models
there is a phantom crossing of there is a singularity of both occur typically at low z when 1m
DEwDEw
phantom DE
standard DE
baRRf )()(
L.A., S. Tsujikawa, 2007
SAIT 2008
What do we need to test DE?
1) observations at z~1
2) observations involving background and perturbations
3) independent, complementary probes
DE observations checklist
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Why z~1
probes at z=0 and z=1000
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Why background+perturbations
The background expansion only probes H(z)
The (linear) perturbations probe first-order quantities
Full metric reconstruction at first order
)])(21()21[( 222222 dzdydxdtads
),(),()( zkzkzH
SAIT 2008
Why independent probes
a) systematics: because we need to test systematics like evolutionary effects in SN Ia, biasing effects in the baryon acoustic oscillations, intrinsic alignments in lensing, etc.b) theory: because in all generality we need to measure two free functions at pert. level (in addition to H(z) at background level)
SAIT 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
SAIT 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
SAIT 2008
Growth of fluctuationsas a measure of modified gravity
we parametrizeInstead of
LCDMDE
DGPST
is an indication of modified gravity
0),(4')'
1('' kkk akGQH
H good fit Peebles 1980Lahav et al. 1991Wang et al. 1999Bernardeau 2002L.A. 2004Linder 2006
Di Porto & L.A. 2007
SAIT 2008
Present constraints on gamma
Viel et al. 2004,2006; McDonald et al. 2004; Tegmark et al. 2004
s≡ d lo g δ /d lo g a
Present constraints on gamma
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Present constraints on gamma
C. Di Porto & L.A. Phys.Rev. 2007
DGP
LCDM
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Observables
222 ),(),( bzkPbzkP mattgal
2)(),( zkPellipt
Correlation of galaxy positions:galaxy clustering
Correlation of galaxy ellipticities:galaxy weak lensing
Correlation of galaxy velocities:galaxy peculiar field
2.. )
'(),(
bzkP velpec
SAIT 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
SAIT 2008
The EUCLID theorem
2.. )
'(),(
bzkP velpec
),( zkPellipt
reconstructing in k,z requires
An imaging tomographic surveyand a spectroscopic survey:
Ψ ,Φ ,b
THE EUCLID THEOREM:
222 ),(),( bzkPbzkP mattgal
2)(),( zkPellipt
Correlation of galaxy positions:galaxy clustering
Correlation of galaxy ellipticities:galaxy weak lensing
Correlation of galaxy velocities:galaxy peculiar field
),(),,( .. zkPzkP velpecgal
SAIT 2008
DUNE x SPACE = EUCLID
- a satellite mission that merges DUNE and SPACE proposals- one of 4 mission selected by ESA Cosmic Vision in 2007- final selection 2011- launch 2015-2020, 5 years duration, half-sky- an imaging mission in several bands optical+NIR (>1 billion galaxies)- a spectroscopic survey: 500.000.000 galaxy redshifts- a pan-european collaboration
30CPS Review CNES Paris
Requirements for Weak LensingStatistical Requirements:• a 20,000 deg2 survey at high galactic latitude (|b|>30 deg) • sample of at least 35 galaxies/amin2 usable for weak lensing (SNR[Sext]>7,
FWHM>1.2FWHM[PSF]) with a median z~1 and an rms shear error per galaxy of
=0.35 (or equivalent combination)• a PSF FWHM smaller than 0.23’’ to be competitive with ground based surveys• photometric redshifts to derive 3 redshift bins over the survey area (from ground
based observations)
Systematics Requirements:• Survey scanned in compact regions <20 on a side, with 10% overlap between
adjacent stripes• a precision in the measurement of the shear after deconvolution of the PSF better
than about 0.1%. This can be achieved with a PSF with a FWHM of 0.23’’, an
ellipticity |e|<6% with an uncertainty after calibration of |e|<0.1%.• good image quality: low cosmic ray levels, reduced stray light, linear and stable
CCDs, achromatic optics
• Photometric redshifts with precision ∆z<0.1 in a subset of the survey to place limits
on the intrinsic correlations of galaxy shapes (from ground based observations)
31CPS Review CNES Paris
Science from DUNE/EUCLID
• Primary goal: Cosmology with WL and SNe
– Measurement of the evolution of the dark energy equation of state (w,w’) from z=0 to ~1
– Statistics of the dark matter distribution (power spectrum, high order correlation functions)
– Reconstruction of the primordial power spectrum (constraints on inflation)
• Cross-correlation with CMB (Planck)
– Search for correlations of Galaxy shear with ISW effect, SZ effect, CMB lensing
– Search for DE spatial fluctuations on large scales
• Study of Dark Matter Haloes:
– Mass-selected halo catalogues (about 80,000 haloes) with multi- follow-up (X-ray, SZ,
optical) halo mass calibration
– Strong lensing: probe the inner profiles of haloes
• Galaxy formation:
– Galaxy bias with galaxy-galaxy and shear-galaxy correlation functions
– Galaxy clustering with high resolution morphology
• Core Collapse supernovae:
– constraints on the history of star formation up to z~1
• Fundamental tests:
– Test of gravitational instability paradigm
– Dark Energy clustering
– Distinguish dark energy from modification of gravity
32CPS Review CNES Paris
Weak Lensing Power Spectrum Tomography
DUNE baseline: 20,000 deg2, 35 galaxies/amin2, ground-based photometry for photo-z’s, 3 year WL survey
z>1
z<1
Redshift bins from photo-z’sWL power spectrum for each z-bin
The power of WL
SAIT 2008
The power of WL
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Probing gravity with weak lensing
In General Relativity, lensing is causedby the “lensing potential”
and this is related to the matter perturbationsvia Poisson’s equation. Therefore the lensing signal depends on two modified gravity functions
and in the growth function
in the WL power spectrum
{
SAIT 2008
Forecasts for Weak Lensing
L.A., M. Kunz, D. Sapone JCAP 2007
Marginalization over the modified gravity parameters
does not spoil errors on standard parameters
)1/()( 0 zzwwzw a
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Weak lensing measures Dark Gravity
DGP Phenomenological DE
Weak lensing tomography over half sky
LCDM
DGP
L.A., M. Kunz, D. Sapone arXiv:0704.2421
Σ0
SAIT 2008
Non-linearity in WL
Weak lensing tomography over half sky
ell_max=1000,3000,10000
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Non-linearity in BAO
Matarrese & Pietroni 2007
SAIT 2008
Clustering measures Dark Gravity
Galaxy clustering at 0<z<2 over half sky ....if you know the bias to 1%
SAIT 2008
Combining P(k) with WL
Weak lensing/ BAO over half sky
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Conclusions
Two solutions to the DE mismatch: either add “dark energy” or “dark gravity” The high precision data of present and near-future allow to test for dark energy/gravity It is crucial to combine background and perturbations A full reconstruction to first order requires imaging and spectroscopy Let EUCLID fly...
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