Modified dark gravity

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• Modified (dark) gravity
• Roy Maartens, Portsmouth

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or Dark Gravity?
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LCDM fits the data well but we cannot explain it

• its the simplest model
• compatible with all data so far
• no other model is a better fit
• but . theory cannot explain it
• why so small?
• and why
• so fine-tuned?

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minimalist approach

• LCDM is
• the best model
• test this against data
• wait for particle physics/QG to explain
• focus on
• the best tests for w-1
• the role of theoretical assumptions
• e.g. wconst,
• curvature0

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but we can do more with the data We can
test gravity The problem is so big that we need
to test alternatives
alternatives to LCDM

• Dynamical Dark Energy in General Relativity
• quintessence,
• effective Dark Energy via nonlinear effects of
  structure formation?
• Dark Gravity Modify GR on large scales
• 4D scalar-(vector)-tensor theories e.g. f(R)
• higher-D braneworld models e.g. DGP

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• NB these alternatives require that the
• vacuum energy does not gravitate
• Dark Energy dynamics
• Dark Gravity dynamics

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is GR wrong on large scales ? i.e. acceleration
via the weakening of gravity
Modified (dark) gravity

• Example from history
• Mercury perihelion
• Newton dark planet ?
• no modified gravity!
• Today
• Modified Friedman equations (schematic)

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• modified
• Friedman
• Examples
• f(R) modified gravity
• DGP modified gravity (5D braneworld model)

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• modified
• Friedman
• general feature
• geometric tests on their own cannot distinguish
  modified gravity from GR
• why?
• geometric tests are based on the comoving
  distance
• - the same H(z) gives the same expansion history

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• we can find a GR model of DE
• to mimic the H(z) of a modified gravity theory
• how to distinguish DG and DE models that both
  fit observed H(z)?
• they predict different rates of growth of
  structure

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• structure formation is suppressed by acceleration
  in different ways in GR and modified gravity
• in GR because DE dominates over matter
• in DG because gravity weakens
• (G determined
• by local physics)

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Distinguish DE from DG via growth of structure
DE DG models LCDM

• DE and DG with
• the same H(z)
• rates of growth of structure differ
• bias evolution?

DG model (modification to GR) DE model (GR) LCDM
f
(Y Wang, 0710.3885)
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f(R) gravity

• simplest scalar-tensor gravity
• a new light scalar degree of freedom
• eg. at low energy,
• 1/R dominates
• This produces late-time self-acceleration
• but the light scalar strongly violates solar
  system constraints
• all f(R) models have this problem
• way out chameleon mechanism, i.e. the scalar
  becomes massive in the solar system
• - very contrived

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Generalising f(R) gravity

• Scalar-tensor gravity (extended quintessence)
• also a new light scalar degree of freedom
• But now there are 2 free functions
• late-time self-acceleration is possible
  without violating solar system constraints
• (no chameleon is needed)
• Interesting - but the models do not improve on
  standard GR quintessence models
• Scalar-vector-tensor gravity even more
  complicated no advantage unless it solves the DM
  and DE problems gravitationally

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Dark gravity from braneworlds?

• String theory - our 4D universe may be moving in
  10D spacetime
• ST unifies the
• 4 interactions

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• new massive graviton modes
• new effects from higher-D fields and other branes
• perhaps these could dominate at low energies

different possibilities bulk fields as
effective DE on the brane (eg
ekpyrotic/ cyclic) matter on a shadow brane
as effective DE on the visible brane
effective 4D gravity on the brane modified on
large scales (eg DGP)
our brane
extra dimension
shadow brane
gravity dilaton, form fields
matter
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DGP the simplest example
4D brane universe in 5D bulk
Friedman on the brane

• early universe recover GR dynamics
• late universe acceleration without DE
• gravity leaks off the brane
• therefore gravity on the brane weakens
• passes the solar system test DGP GR
• The background is very simple like LCDM

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Expansion history

• Density perturbations (sub-horizon)
• (cannot neglect 5D effects!)
• More suppression of
• structure than LCDM

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too good to be true

• 5D analysis of perturbations shows
• - there is a ghost in the scalar sector of the
  gravitational field
• This ghost is from 5D gravity
• It is not apparent in the background
• It is the source of suppressed growth
• The ghost makes the quantum vacuum unstable
• Can DGP survive as a classical toy model?

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The simplest models fail

• f(R) and DGP simplest in their class
• simplest modified gravity models
• both fail because of their scalar degree of
  freedom
• f(R) strongly violates solar system constraints
• DGP has a ghost in 5D gravity
• Either GR is the correct theory on large scales
• Or Modified gravity is more complicated

THEORY find a ghost-free generalized DGP or
find a non-ugly ST model ?
PHENOMENOLOGY model-independent tests of
the failure of GR ?
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Model-independent tests of GR

• There is no natural DE model in GR
• (but LCDM is preferred by simplicity)
• There is no natural or preferred modified MG
• (theory gives no guidance)
• Aim without choosing a DE model in GR, and
  without specifying a modified DG model, try to
  find constraints on deviations from GR
• Problem find tests that do not depend on the DE
  or the DG model
• In parallel
• 1. Test for Lambda vs dynamical DE in GR
• 2. Test for GR vs modified DG

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• Some complications
• modified gravity has dark anisotropic stress
• examples
• DE (smooth) only need growth rate for CMB,LSS
• DG also need anisotropic stress Geff
• linear-nonlinear transition
• (nonlinear regime should recover GR)
• can severely complicate WL tests

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• Degeneracies
• DE with clustering and anisotropic stress
  can look like MG (physical?)
• astrophysical (eg bias evolution vs growth
  rate)
• Approaches
• (1) Growth rate
• compare the observed growth rate with the
  theoretical rate is it DE or DG?
• we need to know the DE and the DG models

f
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• (2) Parameter-splitting
• check for a breaking of GR consistency
  between geometry and growth
• eg
• inconsistency could
• mean a more
• complicated DE
• model or data
• problems

CMB CMBGal CMBSN CMBWL All
(S Wang et al, 0705.0165)
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• (3) Parametrised post-Friedman approach
• Parametrised post-Newtonian formalism has been
  very successful for testing deviations from GR in
  the solar system
• Develop a PPF for modified DG?
• Need basic assumptions
• DE is smooth
• modified gravity is a metric theory with
  energy conservation
• To close the system 3 functions
• (Hu, Sawicki 0708.1190 Jain, Zhang 0709.2375)

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some conclusions

• observations imply acceleration
• theory did not predict it and cannot explain it
• simplest model LCDM is the best we have
• GR with dynamical DE no natural model
• modifications to GR dark gravity
• theory gives no natural model
• simple f(R) model fails solar system test
• simplest braneworld model DGP has a ghost
• theorists need to keep exploring
• better models
• better observational tests
• (model-independent?)