of gravity

1
of gravity
The dark side

• Luca Amendola
• INAF/Osservatorio Astronomico di Roma

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Observations are converging
to an unexpected universe
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Can we detect traces of modified gravity at
Modified gravity
background linear level
? non-linear


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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
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Cosmology and modified gravity
very limited time/space/energy scalesonly
baryons

in laboratoryin the solar systemat
astrophysical scalesat cosmological scales
complicated by non-linear/non-gravitational
effects
unlimited scales mostly linear
processesbaryons, dark matter, dark energy !
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Simplest MG (I) DGP

• L crossover scale
• 5D gravity dominates at low energy/late
  times/large scales
• 4D gravity recovered at high energy/early
  times/small scales

(Dvali, Gabadadze, Porrati 2000)

5D Minkowski bulk infinite volume extra dimension
brane
gravity leakage
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Simplest MG (II) f(R)

Lets start with one of the simplest MG model
f(R)
eg higher order corrections

• 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

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Is this already ruled out by local gravity?
is a scalar-tensor theory with Brans-Dicke paramet
er ?0 or a coupled dark energy model with
coupling ß1/2
a
(on a local minimum)
?
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The simplest case
Turner, Carroll, Capozziello etc. 2003
In Einstein Frame
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R-1/R model the fMDE
today
mat
rad
field
rad
mat
field
?MDE
In Jordan frame
Caution Plots in the Einstein frame!
instead of !!
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Sound horizon in RRn model
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?
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MG in the background (JF)
An autonomous dynamical system
characteristic function
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Classification of f(R) solutions
For all f(R) theories, define the characteristic
curve
deSitter acceleration, w -1 General
acceleration, any w
wrong matter era (t1/2) good matter era (t2/3)
for m0
The problem is can we go from matter to
acceleration?
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The m,r plane
The qualitative behavior of any f(R) model can
be understood by looking at the geometrical
properties of the m,r plot
matter era
deSitter
m(r) curve
acceleration
crit. line
The dynamics becomes 1-dimensional !
L.A., D. Polarski, S. Tsujikawa, PRD,
astro-ph/0612180
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The power of the m(r) method
REJECTED
REJECTED
REJECTED
REJECTED
REJECTED
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The triangle of viable trajectories
There exist only two kinds of cosmologically
viable trajectories
Notice that in the triangle mgt0
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A theorem on viable models
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

standard DE
phantom DE
L.A., S. Tsujikawa, 2007
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Local Gravity Constraints are very tight
Depending on the local field configuration
depending on the experiment laboratory, solar
system, galaxy
see eg. Nojiri Odintsov 2003 Brookfield et al.
2006 Navarro Van Acoyelen 2006 Faraoni 2006
Bean et al. 2006 Chiba et al. 2006 Hu, Sawicky
2007....
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LGCCosmology
Take for instance the ?CDM clone
Applying the criteria of LGC and Cosmology
i.e. ?CDM to an incredible precision
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However. . . perturbations
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Two free functions

• At the linear perturbation level and sub-horizon
  scales, a modified gravity model will

• modify Poissons equation
• induce an anisotropic stress

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MG at the linear level

• standard gravity

Boisseau et al. 2000 Acquaviva et al. 2004 Schimd
et al. 2004 L.A., Kunz Sapone 2007

• scalar-tensor models

• f(R)

Bean et al. 2006 Hu et al. 2006 Tsujikawa 2007

• DGP

Lue et al. 2004 Koyama et al. 2006

• coupled Gauss-Bonnet

see L. A., C. Charmousis, S. Davis 2006
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Parametrized MG Growth of fluctuationsas a
measure of modified gravity
Peebles 1980 Lahav et al. 1991 Wang et al.
1999 Bernardeau 2002 L.A. 2004 Linder 2006
good fit
we parametrize
Instead of
LCDM DE DGP ST
Di Porto L.A. 2007

is an indication of modified gravity/matter
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Present constraints on gamma
Viel et al. 2004,2006 McDonald et al. 2004
Tegmark et al. 2004
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Present constraints on gamma
LCDM
DGP
C. Di Porto L.A. 2007
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Two MG observables
Correlation of galaxy positions galaxy
clustering
Correlation of galaxy ellipticities galaxy weak
lensing
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Probing gravity with weak lensing
Statistical measure of shear pattern, 1
distortion
Background sources
Dark matter halos
Observer

• Radial distances depend on
• geometry of Universe

• Foreground mass distribution depends on
  growth/distribution of structure

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Probing gravity with weak lensing
In General Relativity, lensing is caused by the
lensing potential
and this is related to the matter
perturbations via Poissons equation. Therefore
the lensing signal depends on two modified
gravity functions


in the WL power spectrum
and in the growth function
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Forecasts for Weak Lensing
Marginalization over the modified gravity
parameters does not spoil errors on standard
parameters
L.A., M. Kunz, D. Sapone JCAP 2007
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Weak lensing measures Dark Gravity
DGP
Phenomenological DE
DGP

LCDM
Weak lensing tomography over half sky
L.A., M. Kunz, D. Sapone arXiv0704.2421
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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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Non-linearity in WL
1000,3000,10000

Weak lensing tomography over half sky
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Non-linearity in BAO

Matarrese Pietroni 2007
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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/gravity
• New MG parameters ?,S
• A general reconstruction of the first order
  metric requires galaxy correlation and galaxy
  shear
• Let EUCLID fly...

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Current Observational Status CFHTLS
Hoekstra et al. 2005 Semboloni et al. 2005
Weak Lensing
First results From CFHT Legacy Survey with
Megacam (wconstant and other priors assumed)
Type Ia Super- novae
Astier et al. 2005