Large%20distance%20modification%20of%20gravity%20and%20dark%20energy

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Large distance modification of gravity and dark
energy

• Kazuya Koyama
• ICG, University of Portsmouth

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Cosmic acceleration

• Cosmic acceleration
• Big surprise in cosmology
• Simplest best fit model
• LCDM
• 4D general relativity cosmological const.

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• 3 independent data sets intersect
  

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Problem of LCDM

• Huge difference in scales (theory vs observation)
• vacuum energy 0 from fundamental theory
• (1) tiny vacuum energy is left somehow
• (2) Potential energy of quintessence field

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Alternative models

• Tiny energy scale
• unstable under quantum corrections
• Alternative - modified gravity
• dark energy is important only at late times
• large scales / low energy
  modifications
• cf.
• from Newton to GR

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• Is cosmology probing breakdown of GR on large
  (IR) scales ?

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Options

• Modify the Friedmann equation empirically
• or
• how to perturb?
• Modify the Einstein-Hilbert action
• cf.

(Freese, )
(Dvali and Turner, )
(Carol et.al., )
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Problems of IR modification

• Modified gravity
• graviton has a scalar mode
• Solar system constraints - theory must be
  GR
• cf.
• difficult to explain dark energy purely from
  modified gravity

(Chiba)
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DGP model
(Dvali, Gabadadze,Porrati)

• Crossover scale
• 4D Newtonian gravity
• 5D Newtonian gravity

gravity leakage
Infinite extra-dimension
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Consistent with local experiments?

• DGP also has a scalar mode of graviton
• 4D Newtonian but not 4D GR!
• (Scalar-Tensor theory)
• Non-linear shielding
• theory becomes GR at
• solar-system
• constraints can be evaded if

5D
ST
GR
4D
(Deffayet et.al.)
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Cosmology of DGP

• Friedmann equation
• early times 4D Friedmann
• late times
• As simple as LCDM model
• and as fine-tuned as LCDM
  
• (stability against quantum corrections can be
  different)

(Deffayet)
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LCDM vs DGP

• Can we distinguish between DGP and LCDM ?
• Friedmann equation
• cf. LCDM

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SNe baryon oscillation

• SNLS SDSS Gold set SDSS

(Maartens and Majerotto in preperation)
(Fairbairn and Goobar astro-ph/0511029)
(cf. Alam and Sahni, astro-ph/0511473)
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Why baryon oscillation?

• Baryon oscillation
• angular diameter at z0.3
• shape parameter of power spectrum
• K0
• equivalent to dark energy model with

(Lue.et.al)
(LCDM)
VS
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DGP Cosmology

• As simple as LCDM
• a falsifiable model
• now the model is under pressure from the
  data
• measurements of is crucial
• Fit to SNe assuming flat universe
• A parameter is fixed!

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Dark energy vs DGP

• Can we distinguish between dark energy in GR and
  DGP ?

DGP model is fitted by
DGP
(Linder)
Dvali and Turner
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Cosmology as a probe of DGP gravity
linear
Non-linear
Scalar tensor
Einstein
4D
5D
CMB SNe
CMB ISW LSS
Weak lensing
Expansion history
Growth rate
Non-linear mapping
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Growth rate of structure formation

• Evolution of CDM over-density
• GR
• If there is no dark energy
• dark energy suppresses the gravitational
  collapse
• DGP
• an additional modification from the scalar
  mode

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Expansion history vs growth rate

• Growth rate resolves the degeneracy

(Lue.et.al, Linder)
LCDM
dark energy
DGP
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Experiments
(Ishak et.al, astro-ph/0507184)

• ASSUME our universe is DGP braneworld
• but you do not want to believe this,
• so fit the data using dark energy model

m(z) apparent magnitude R CMB shift
parameter G(a) Growth rate
OR
SNeCMB SNeweak lensing
Inconsistent!
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Consistent 5D analysis of growth factor
KK and R.Maartens astro-ph/0511634

• Use correct 5D physics
• growth rate is sensitive to truncation of 5D
  physics
• Consistency in 5D physics
• (1)
• Analysis based on (2)
• must be revisited

(1) Lue.et.al astro-ph/0401515 (2) Song
astro-ph/0407489
LCDM
Dark energy
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Solutions for metric perturbations
(Lue et.al, KK and R,Maartens)

• Solutions for metric perturbations
• Scalar tensor theory with Brans-Dick parameter

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ISW effects and weak lensing

• Growth rate is determined by
• ISW effects and weak lensing effects depends on
• the same as GR!
• Difference comes from growth rate of

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Large scale ISW
Non-linear P(k)
Need 5D solutions
Need non-linear mapping
linear
Non-linear
Scalar tensor
Einstein
4D
5D
CMB ISW LSS
CMB SNe
Weak lensing
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Summary

• Alternative to LCDM from large scale modification
• DGP model as an example
• The model is already in tension with the data
  
• Structure formation is different from GR
• 5D study of perturbations is crucial
• cf. Theoretical difficulties of DGP model
• strong coupling / a ghost in de Sitter
  spacetime

(Luty, Porrati, Rattazi) (Nicolis, Rattati KK
hep-th/0503191
Gorbunov, KK, Sibiryakov to appear)
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Lessons from DGP

• Gravity is subtle
• modification at present day horizon scale
  does
• not mean no modification under horizon
• structure formation is different from GR
• great opportunity to exploit future
  observations
• Build consistent models
• Structure formation is sensitive to
  underlying theory
• Build consistent theory (ghost free etc.)
• Address fundamental questions (fine-tuning,
  coincidence)