Luca%20Amendola

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The dark side of gravity

• Luca Amendola
• INAF/Osservatorio Astronomico di Roma

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Why DE/MG is interesting
g
How to observe it
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Observations are converging
to an unexpected universe
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Classifying the unknown
Standard cosmology GR gravitational equations
FRW metric

• a) change the equations
• i.e. add new matter field (DE) or modify gravity
  (MG)
• b) change the metric
• i.e. inhomogeneous non-linear effects, void
  models, etc

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Which are the effects of modified gravity at
Modified gravity
background linear level
? non-linear


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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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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
linearized PPN metric with
Conclusion there are solutions which look
Einsteinian but are not
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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)
The simplest MG in 4D 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
?
Adelberger et al. 2005
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The fourfold way out of local gravity

depend on time depend on space depend on local
density depend on species
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Sound horizon in RR - n model
Turner, Carroll, Capozziello etc. 2003
in the Matter Era !
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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MG in the background
O?
OP
OK
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Classification of f(R) solutions
For all f(R) theories
deSitter acceleration, w -1 General
acceleration, any w
wrong matter era (t1/2) good matter era (t2/3)
for m0
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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
cosmologically viable trajectories
Notice that in the triangle mgt0
L.A., D. Polarski, S. Tsujikawa 2007 PRD
astro-ph/0612180
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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 Mota et al. 2006....
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LGCCosmology
c
Take for instance the ?CDM clone
Applying the criteria of LGC and background
cosmology
i.e. ?CDM to an incredible precision
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The background expansion only probes H(z)The
(linear) perturbations probe first-order
quantities
What background hidesperturbations reveal
Full metric reconstruction at first order
requires 3 functions
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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

(most of what follows in collaboration with M.
Kunz, D. Sapone)
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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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Reconstruction of the metric
Correlation of galaxy positions galaxy
clustering
Correlation of galaxy ellipticities galaxy weak
lensing
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Peculiar velocities
Correlation of galaxy velocities galaxy peculiar
field
redshift distortion parameter
?0.700.2
Guzzo et al. 2008
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The Euclid theorem
Observables
Conservation equations
5 unknown variables
We can measure 3 combinations and we have 2
theoretical relations
Theorem lensinggalaxy clustering allows to
measure all (total matter) perturbation
variables at first order without assuming any
particular gravity theory
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The Euclid theorem
Observables
Conservation equations
5 unknown variables
We can measure 3 combinations and we have 2
theoretical relations
Theorem lensinggalaxy clustering allows to
measure all (total matter) perturbation
variables at first order without assuming any
particular gravity theory
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The Euclid theorem
From these we can estimate deviations from
Einsteins gravity
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Euclid
A geometrical probe of the universe proposed for
Cosmic Vision
All-sky optical imaging for gravitational
lensing All-sky near-IR spectra to H22 for BAO


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Weak lensing
Euclid forecast
Present constraints
DGP

LCDM
Weak lensing tomography over half sky
L.A., M. Kunz, D. Sapone arXiv0704.2421 DiPorto
L.A. 2007
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Power spectrum

Galaxy clustering at 0ltzlt2 over half sky
....if you know the bias to 1
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Non-linearity in BAO

Matarrese Pietroni 2007
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Poster advertisement
Cosmic parallax
Garcia-Bellido Haugbolle 2008
See poster by Miguel Quartin Quercellini,
Quartin LA, arXiv 0809.3675
LTB void model
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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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The bright side of Munich

• Luca Amendola
• INAF/Osservatorio
• Astronomico di Roma

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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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References
Basics L.A. , Phys. Rev. D62, 043511,
2000 CMB L.A. , Phys. Rev. Lett.
86,196,2001 Bias L.A. D.
Tocchini-Valentini, PRD66, 043528, 2002 WMAP
astro-ph/0303228, Phys Rev 2003 N-body
A. Maccio et al. 2004 Dilatonic dark energy
L.A., M. Gasperini, D. Tocchini-Valentini, C.
Ungarelli, Phys. Rev. D67, 043512, 2003
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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