1. Some challenges to MOND- like modifications of GR Karel Van Acoleyen, Durham, IPPP

2. It’s hard to modify GR consistently at large distances. Obvious consistency requirements: Agreement with Solar system tests. No instabilities ( ghosts, tachyons,…) In addition we want to get MOND, or something MONDlike.

3. To get MOND (or something MONDlike), we need a new dimensionful parameter in the gravitational action. (Even if the MOND scale is connected to the cosmic background, one will still need this scale to set the late time cosmic acceleration)

4. TeVeS ++ Gives MOND! ( a_0 is set by l ) + No obvious instabilities, BUT watch out for the gauge variant vectorfields. + Safe with Solar System tests. (for certain choices of ) -Is the theory consistent at the quantumlevel: What to do with the gaugevariant vectorfields and the lagrangemultipliers. Is the form of protected under quantumcorrections?

5. Logarithmic actions. + one scale gives late time cosmic acceleration and at the same time gives departure from Newtonian gravity at accelerations. + No instabilities at the perturbative level. + Safe with Solar system experiments. (But predicts effects that will be tested in the near future). -So far we can not say much at the non-perturbative level. Can we actually get MOND? Do we really have no instabilities at the non-perturbative level? -What about the quantumcorrections to this action?

6. Conformal gravity. Because of the conformal symmetry there is NO SCALE at all! no MOND scale But also no massive particles (like a proton, a planet, a star,…): conformal symmetry: The Schwarzschild solution of Mannheim and Kazanas corresponds to a traceless source, NOT to a static mass source like a planet, a star, the centre of galaxy,... No solutions for massive sources

7. Conformal gravity. Do we know for sure that:, for a massive particle? Yes, particles follow geodesics

8. Conformal gravity. We can introduce conformal symmetry in the matter sector, but we will have to spontaneously break it, to generate massive particles. This will result in Einstein gravity+ a Weyl term. This theory gives a proper Newtonian limit as long as !!. In addition the Weyl term gives rise to a ghost with and corrections at short distances.

9. Conformal gravity. No conformal invariance: We can trivially get a conformal invariant action, through the introduction of a spurious scalar field: The action will then obviously have the conformal symmetry:

10. Conformal gravity. This action is physically equivalent to the one we started with. (Einstein Gravity+ordinary matter+weyl term.) : The E.O.M. only determine and. is a spurious (gauge) degree of freedom. Fix the gauge, and we’re back at the beginning. ( ). Bottomline: Conformal gravity is inconsistent with nature unless you break it spontaneously, you’re then left with ordinary gravity+ the Weyl term and there will be no modification at large distances.

11. Scalar-Tensor-Vector-Gravity -The formula does NOT follow from the theory. -The variation of the parameters over different length scales does NOT follow from the theory.