1. Categorizing Approaches to the Cosmological Constant Problem
Stefan Nobbenhuis
Supervisor: Prof. G. ’t Hooft
August 28th 2005
COSMO-05, Bonn.
gr-qc/

2. The Problem in Threefold Contribution to vacuum Energy!
= -1 for CC
1) Unnatural values
2) Why not exactly zero?
3) Cosmic Coincidence Problem
Contribution to vacuum Energy!

3. To curve vacuum spacetime costs a lot of energy,
whereas stretching it, is (almost) for free…
© Gerard ’t Hooft
This is unusual, for most ordinary stuff,
stretching it is much harder than curving it!

4. Type I: Symmetry Principle Type I: Symmetry Principle
Type II: Backreaction
SUSY
Imaginary Space
Energy  - Energy
Conformal Symmetry
Holography
Sub/super-Planckian
Other universes…
Instabilities of dS-space
Scalar field
Gravitons
RG-Group Running
Trace Anomaly
BH production
Type 0: Just Fine-tuning
2) Beyond QM
1) Beyond 4D
Type III: Violating
Equivalence Principle
Type IV: Statistical Distribution
Anthropic Principle
Discrete
Continue
Wavefunction of the universe
Wormholes
Massive Gravitons
Ghost Condensation
Graviton as Goldstone Boson
Fat Gravitons

5. Symmetry Argument
Supersymmetry
Vanishing vacuum energy if SUSY is unbroken
SUGRA
In D = 2+1 the ground state can be exactly supersymmetric without supersymmetric excited states
(Witten (1994))
Generically supercurrents are covariantly conserved:
But in the presence of a covariantly constant spinor,
a conserved current can be constructed and therefore a conserved supercharge: m
However, in 2+1 dimensions, any mass m produces a conical spacetime
at space infinity: no killing spinors exist!

6. Consider the following transformation:
Imaginary space
Consider the following transformation:
So if we postulate this transformation as a symmetry, a CC-term is forbidden!
A deeper reason could be a change of our boundary conditions. Normally we quantize a field by putting it in a box and impose periodic boundary conditions on its real coordinates.

7. What happens if we impose boundary conditions on imaginary parts?Re
Positive energy particles transform into negative energy particles
Main problem however, is that masses seem to be forbidden now:
This results from ‘first’ quantization:
Which explicitly violates the symmetry…
Higgs Mechanism?
3+3 dimensional spacetime?

8. Modifications of General Relativity
Infinite volume extra dimensions
V(r) ~ 4D for r < rc
~ 5D for r > rc
For N > 2, H decreases as  increases!
For N > 2, solutions can be paramtetrized as:

9. Unclear whether it is viable!
Infinite volume extra dimensions
brane
singularity yg
However, the extra d.o.f., the ‘brane bending mode’ becomes strongly coupled,
resulting in a breakdown of the effective theory: the physics becomes sensitive
to the unknown UV completion of the theory.
This is a much more general phenomenon, changing a theory in the IR by
adding a new d.o.f. often leads to strong coupling of this d.o.f. in the UV.
Reason here is that the new scalar has no kinetic terms, but does have cubic and
higher order interactions terms.
Unclear whether it is viable!

10. Conclusions
So far none of the approaches stands out as a serious candidate for a solution
Severeness fine-tuning seems to indicate to more than just a philosophical point
No satisfactory symmetry principle available that can explain smallness of CC
Supersymmetry does not seem to help
If CC non-zero nowadays, a back-reaction mechanism might be favorable,
but these generally are either too weak, or lead to inconsistencies.
Near-future experiments will fortunately help end some speculations