of gravity

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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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The dark energy problem
gravity matter
Solution modify either the Matter sector
DE
or the Gravity sector
MG
...but remember
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Modified matter
Problem All the matter particles we know possess
an effective interaction range that is much
smaller the cosmological ones
the effective pressure is always positive !
Solution add new forms of matter with strong
interaction/self-interaction
the effective pressure can be large and negative
Dark Energyscalar fields, generalized perfect
fluids etc
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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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f(R) is popular....

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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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Dark Fog
The trouble with f(R) its Fourth Order
Gravity (FOG) ! Higher order equations
introduce new solutions (acceleration ?) new
instabilities (is the universe stable?)
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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
...and by the way
L.A., D. Polarski, S. Tsujikawa, PRL 98, 131302,
astro-ph/0603173
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WMAP and the coupling ?
Planck ?????????
L.A., C. Quercellini et al. 2003
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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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Constraints on viable trajectories
Cosmological constraints
Constraint from accelerated expansion SN
require m(present)lt0.1
Constraint from the matter expansion CMB peak
requires m(past)lt0.1
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Viable trajectories are cool !
Viable trajectories have a very peculiar
effective equation of state
Define wDE implicitely as
We find
Theorem diverges if
grows in the past, i.e. if
Corollary all viable f(R) cosmologies possess a
divergent
L.A., S. Tsujikawa, 2007
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Phantom crossing
Conclusions 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
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Crossing/singularity as signatures of modified
gravity
The same phenomenon occurs for

• Scalar,Vector, Tensor models (Libanov et al.
  2007)

• DGP (Alam et al 2005)

• and in the Riess et al. (2004) dataset !!

Nesseris Perivolaropoulos 2005
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...but dont forget theLocal Gravity
Constraints...
However, if we apply naively the LGC at the
present epoch.
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relaxing the Local Gravity Constraints ?
However, the mass depends 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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MG at the linear level

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

• modify Poissons equation
• induce an anisotropic stress
• modify the growth of perturbations

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MG at the linear level

• standard gravity

Boisseau et al. 2000 Acquaviva et al. 2004 Schimd
et al. 2004

• 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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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 the two modified
gravity functions

in the WL power spectrum
and in the growth function
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Growth of fluctuations
A good fit to the linear growth of fluctuations
is
Peebles 1980 Lahav et al. 1991 Wang et al.
1999 Bernardeau et al. 2002 L.A. 2004 Linder
2006
where
LCDM DE DGP ST

we parametrize
Instead of
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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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Weak lensing measures Dark Gravity
Marginalizing over modified gravity parameters
FOM

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Non-linearity
N-Body simulations
Higher-order perturbation theory
Maccio et al. 2004 Jain et al. 2006 ....
Kamionkowski et al. 2000 Gaztanaga et al.
2003 Freese et al. 2002 Makler et al. 2004 Lue et
al. 2004 L.A. C. Quercellini 2004 ....
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N-body simulations in MG
Dark energy/dark matter coupling

• Two effects DM mass is varying, G is different
  for baryons and DM

mb
mc
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N-body simulations
?
ß0.15
ß0.25
A. Maccio, L.A.,C. Quercellini, S. Bonometto, R.
Mainini 2004
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N-body simulations
ß0.25
ß0.15
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N-body simulations halo profiles
ß-dependent behaviour towards the halo center.
Higher ß smaller rc
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Conclusions the teachings of DE

• There is much more than meets the eyes in the
  Universe
• 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
• It is crucial to combine background and
  perturbations
• Weak Lensing is a good bet...(to be continued)

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An ultra-light scalar field
Hubble size
Galactic size
Adopting a PNGB potential
Abundance
Mass
L.A. R. Barbieri 2005
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Dark energy as scalar gravity
Jordan frame
Einstein frame
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An extra gravity
Newtonian limit the scalar interaction generates
an attractive extra-gravity

in real space
Yukawa term
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Understanding dark energy
Let him who seeks continue seeking until he
finds. When he finds, he will become troubled.
When he becomes troubled, he will be astonished
Coptic Gospel of Thomas
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An ultra-light scalar field
Hubble size
Galactic size
Adopting a PGB potential
Abundance
Mass
L.A. R. Barbieri 2005