On Modifying Gravity

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On Modifying Gravity

• Pedro G. Ferreira
• University of Oxford

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Collaborators

• Celine Boehm (Annecy)
• D. Mota (Heidelberg)
• C. Skordis (Perimeter Institute)
• G. Starkman (Case Western Reserve)
• T. Zlosnik (Oxford)

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Roadmap

• The problem with gravity (dark matter or modified
  gravity)
• Bekensteins proposal for a covariant theory
  TeVeS
• Perturbations in TeVes
• The time-like vector the Aether
• Conclusions

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NGC 3198
Keplerian
Begeman 1987
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Density Perturbations
Three Regimes

• Tight coupling
• Recombination
• Free Streaming

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Dark Matter
If
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Alternative solution to rotation curve problem
Milgrom, 83
constant
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Modified theory of gravity
Rewrite as
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Many successes but problems

• Clusters mass to light is too large
• Dwarf Galaxies have large tidal radii
• No Birkhoff theory (how do you do N-body?)
• Silk damping?
• Non-relativistic

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How to build relativistic theory basic idea
Gravity
Dynamics
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Relativistic version
Dynamics (geodesic equation)
Gravity (Einstein equations)
Common metric
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Bimetric theories
Use two different metrics
Geometric metric in Einstein equations
Physical in Geodesic equations
Bekenstein, 04
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A theory (TeVeS)
constants
Lagrange multipliers
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How do we get modified gravity?
Physical potential Geometric potential
Scalar Field Equation
Lagrange multiplier
Low energy/non relativistic limit is MOND
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Cosmology
Skordis et al, 2006
Two metrics two scale factors
Physical Geometric
where
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Cosmological Tracking
If
then
Rad. era
Matter or c.c. era
BBN
Not Dark Matter
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Perturbations definitions
Scalar Field
Vector Field
(scalar modes)
Metric
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Perturbations evolution
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Solution to vector
Approximation
with
where
So growth of is enhanced.
Result growth of and
Dodelson and Liguori, 2006
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Need to fit peaks
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Main points

• Can generate large scale structure (in a flat
  universe, need neutrinos)
• Vector field plays an essential role
• may be smoking gun for these
  theories

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Simplify this theory

• Solve constraint
• Rewrite action solely in terms of physical metric
  and vector field

Zlosnik, Ferreira Starkman, 2006
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The Aether
Timelike vector
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Equations of motion
Simplest case
Jacobson, Mattingley, Forster, Carroll, Lim
(1999-2006)
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How do we modify gravity?

• Take non-relativistic, weak field limit

Examples
Rescale G
MONDian
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Tests

• MONDian behaviour
• Solar system constraints
• Causal, non-tachyon, subluminal propagation
• Cosmological (FRW behaviour)

In Progress

• PPN calculation
• Weak Lensing
• Cosmological perturbations

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Conclusions and comments

• Vector-Tensor theory can have growing mode
  (TeVeS)
• Perturbation in vector, , MUST be considered
• Working out GENERAL features
• Is the smoking gun?
• Does not satisfy Birkhoffs theorem
• Severe tests it must pass clusters and satellites

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Stars
Globular Cluster
Dwarf Galaxy