Transcript Some random thoughts on MOND

Some challenges to MONDlike 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:
No solutions for
massive sources
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,...
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
addition the Weyl term gives rise to a ghost with
and corrections at short distances
.
!! . In
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
does NOT follow from the theory.
over different length scales