Categorizing Approaches to the Cosmological Constant Problem Stefan Nobbenhuis Supervisor: Prof. G. ’t Hooft August 28th 2005 COSMO-05, Bonn. gr-qc/0411093.

Categorizing Approaches tothe Cosmological Constant

ProblemStefan Nobbenhuis

Supervisor: Prof. G. ’t Hooft

August 28th 2005

COSMO-05, Bonn.

gr-qc/0411093

The Problem in Threefold

Contribution to vacuum Energy!

= -1 for CC

1) Unnatural values

3) Cosmic Coincidence Problem

2) Why not exactly zero?

To curve vacuum spacetime costs a lot of energy,whereas stretching it, is (almost) for free…

This is unusual, for most ordinary stuff,stretching it is much harder than curving it!

© Gerard ’t Hooft

Type I: Symmetry Principle Type II: Backreaction

Type III: ViolatingEquivalence Principle

Type IV: Statistical Distribution

•Massive Gravitons•Ghost Condensation•Graviton as Goldstone Boson•Fat Gravitons

• SUSY• Imaginary Space• Energy - Energy• Conformal Symmetry• Holography• Sub/super-Planckian• Other universes…

•Instabilities of dS-spaceScalar fieldGravitons

•RG-Group Running•Trace Anomaly•BH production

•Anthropic PrincipleDiscreteContinue

•Wavefunction of the universe•Wormholes

1) Beyond 4D 2) Beyond QM

Type 0: Just Fine-tuning

Type I: Symmetry Principle

Symmetry ArgumentSupersymmetry

SUGRA

Vanishing vacuum energy if SUSY is unbroken

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 spacetimeat space infinity: no killing spinors exist!

In D = 2+1 the ground state can be exactly supersymmetric without supersymmetric excited states

(Witten (1994))

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.

Re

Im

Main problem however, is that masses seem to be forbidden now:

This results from ‘first’ quantization:

Which explicitly violates the symmetry…

What happens if we impose boundary conditions on

imaginary parts?

Higgs Mechanism?

Positive energy particles transform into negative energy particles

3+3 dimensional spacetime?

Modifications of General Relativity

Infinite volume extra dimensions

V(r) ~ 4D for r < rc

~ 5D for r > rc

For N > 2, solutions can be paramtetrized as:

For N > 2, H decreases

as increases!

Infinite volume extra dimensions

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 byadding 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 andhigher order interactions terms.

Unclear whether it is viable!

brane singularityyg

Conclusions

Supersymmetry does not seem to help

No satisfactory symmetry principle available that can explain smallness of CC

If CC non-zero nowadays, a back-reaction mechanism might be favorable, but these generally are either too weak, or lead to inconsistencies.

Severeness fine-tuning seems to indicate to more than just a philosophical point

Near-future experiments will fortunately help end some speculations

So far none of the approaches stands out as a serious candidate for a solution