Pedro G. Ferreira University of Oxford On Modifying Gravity Pedro G. Ferreira University of Oxford

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

Roadmap The problem with gravity (dark matter or modified gravity) Bekenstein’s proposal for a covariant theory: TeVeS Perturbations in TeVes The time-like vector: the “Aether” Conclusions

NGC 3198 Keplerian: Begeman 1987

Density Perturbations Three Regimes Tight coupling Recombination Free Streaming

Dark Matter If

Adiabatic baryonic universe Adiabatic CDM universe Isocurvature baryonic universe

Alternative solution to rotation curve problem Milgrom, 83 constant

Modified theory of gravity Rewrite as:

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

How to build relativistic theory: basic idea Dynamics Gravity

Relativistic version Dynamics Gravity (geodesic equation) (Einstein equations) Common metric

“Bimetric” theories Use two different metrics “Physical” in Geodesic equations “Geometric” metric in Einstein equations Bekenstein, 04

A theory (TeVeS) constants Lagrange multipliers

How do we get modified gravity? Physical potential Geometric potential Scalar Field Equation Lagrange multiplier Low energy/non relativistic limit is MOND

Cosmology Two metrics: two scale factors … where: Physical Geometric Skordis et al, 2006 Two metrics: two scale factors … Physical Geometric where:

Cosmological Tracking If then Rad. era Matter or c.c. era BBN: Not Dark Matter

Perturbations: definitions Scalar Field Vector Field (scalar modes) Metric

Perturbations: evolution

Solution to vector Approximation: with where So growth of is enhanced. Result: growth of and Dodelson and Liguori, 2006

Need to fit peaks

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

“Simplify” this theory Solve constraint: Rewrite action solely in terms of physical metric and vector field Zlosnik, Ferreira & Starkman, 2006

The Aether Timelike vector

Equations of motion Simplest case: Jacobson, Mattingley, Forster, Carroll, Lim (1999-2006)

How do we modify gravity? Take non-relativistic, weak field limit: Examples: Rescale G MONDian

Tests MONDian behaviour Solar system constraints Causal, non-tachyon, subluminal propagation Cosmological (FRW behaviour) In Progress: PPN calculation Weak Lensing Cosmological perturbations

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 Birkhoff’s theorem Severe tests it must pass: clusters and satellites

Stars Globular Cluster Dwarf Galaxy