1. Long distance modifications of gravity in four dimensions.
Karel Van Acoleyen Durham University, IPPP
Work done in collaboration with Ignacio Navarro.
gr-qc/ (Phys. Lett. B 622, 2005)
gr-qc/ (JCAP 03, 2006 )
gr-qc/
In preparation

2. The models
with:

3. Prime motivation: alternatives for Dark Energy
With crossover scale:

4. Propagating degrees of freedom: (on deSitter space)
massless spin 2 graviton
+ extra massive scalar
no ghosts
Effective Planck mass and the mass of the scalar depend on the background !!

5. ‘Schwarzschild’ solution at large distances
On vacuum, the mass of the scalar is very light.
problem for the Solar System tests?
BUT, the perturbation series breaks down at ‘short’ distances:
Corrections go like: with:
This distance is huge: ~10 kpc for the Sun, ~1 Mpc for the Milky Way )

6. ‘Schwarzschild’ solution at short distances
The curvature in the Solar System is huge. So we don’t expect much modification. (We need Q!)
What about the extra scalar? Corrections for
Mass depends on the background:
Explicitly:

7. To summarize:

8. Could the non-perturbative region play the role of the dark matter halo?
Yes! (maybe): in the limit n :
→ Logarithmic actions:

9. Logarithmic actions as an alternative to Dark Energy and Dark Matter halo’s?
For a large class of models there is an enhancement of Newton’s constant at large distances at large distances there seems to be more matter than there actually is .
Typically, there exist deSitter attractors, with the Hubble constant of the order of the crossover scale.
Departure from Newtonian gravity, at a critical acceleration set by the same crossover scale.
MOND?

10. Logarithmic actions testable predictions on Earth!
Mass of the scalar on earth:
short distance corrections at 0.1mm.
Explicit calculation gives an anisotropic correction, for the potential of a probe
mass in the background field of the earth:

11. Conclusions
One can consistently modify gravity at large distances in 4D.
The modification is characterized by:
1. an extra scalar degree of freedom, with a mass that runs with the backgroundcurvature ( ):
2. a running Newton’s constant:
Logarithmic actions have potential to unify the DE and DM problem:
And give testable predictions on Earth.

12. Lots of stuff to do:
Examine the influence on the CMB of the extra scalar+ running Newton’s Constant+Lorentz violation.
Understand the Lorentz violation theoretically;
consistent?
Solve in the non-perturbative intermediate regime
MOND?
…….