Some challenges to MOND-like modifications of GR

Karel Van Acoleyen, Durham, IPPP

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.

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)

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?

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?

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

Conformal gravity.

• Do we know for sure that: , for a massive particle?

Yes, particles follow geodesics

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 .

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:

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.

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.