Observational data indicates that the cosmological constant has a positive value, resulting in a de Sitter spacetime. In loop quantum gravity, the IR divergences in the Ponzano-Regge model can be made to disappear through q-deforming SU(2) to SUq(2). The classical limit of this Turaev-Viro model is GR with positive cosmological constant.
On the other hand, anti de Sitter spacetime has a number of (potentially) desirable properties as well, for example the AdS/CFT correspondence. This correspondence is used in Light Front holographic QCD and seems to offer some insights into confinement as well as meson and hadron spectroscopy (arxiv:1407.8131). AdS also admits a positive energy operator making it more suitable for a particle interpretation. There has been some work (mostly by Flato and Fronsdal) describing photons and leptons as composites of singleton representations that live in an AdS spacetime.
Would it be possible and sensible to describe spacetime as being anti de Sitter at very small scales and de Sitter at cosmological scales? Perhaps this would be possible through a bi-metric model?
To me it seems that such a model would offer the best of both worlds (LQG without IR divergences, agreement with cosmological observations, AdS/CFT, singleton representations). I am just not sure if such a model would be possible and if it even makes sense to think along these lines. I would very much value any comments people may have.
Thanks in advance!
Hi Niels, that is a very interesting suggestion indeed! I can see the advantages too.
Dear Niels,
That would mean that nature behaves differently at different scales.
Either we find a deep reason for this change of behavior:when and where this change takes place or we have to recognize that both the models used are not suitable and need to be changed.
Dear Stefano, you would not imply that nature behaves the same at cosmological scale as it does at the quantum level, now would you?
Niels' suggestion does on the other hand not say WHY it should be that AdS and dS should merge the way he proposes, that is true.
Hi Martin,
Thank you for your comments. I would be keen to know what advantages you see in such an approach. I will send you an e-mail one of these days explaining my ideas a bit more fully as it also relates to some of your research interests.
Dear Stefano,
Thank you for your comment. Like Martin pointed out, nature does behave differently at different scales. I want to know if it is reasonable to have a metric that is also scale dependent.
One of my interests is deformations of algebras as a means of generalizing symmetry. So for example, both SR and QR can be seen as deformations of Galilean relativity and classical mechanics respectively. Taking Minkowski spacetime with Poincare symmetry and deforming it give either dS or AdS. At this point the isometry group is rigid and cannot be deformed further. The mathematics does not tell you the value of the cosmological constant (just as it doesn't tell you the value of x or hbar).
Experiments suggest that at least on large scales the cosmological constant is positive. Loop quantum gravity seems to introduce a positive cosmological constant to rid the theory of IR (large scale) divergences. On the other hand many theories make use of the AdS/CFT correspondence and assume an AdS spacetime. This also gives some impressive results. There is interesting physics in the singleton representations of AdS (discovered by Dirac all the way back in 1963).
My question is whether it is possible to reconcile these approaches. I think that if it is then it could lead to interesting new physics.
Dear Robert, I do agree.
I understand Niels' question in the sense that there may be, for example, a perfect stitch between the putative internal space of elementary particles and the space-time of our cosmos.This would make the internal degrees of freedom of elementary particles like a kind of real internal space. If so, it may iron out a few problems in physics. Let's see!
In this moment I can say only the following: In the solution method, published in paper "Cs. Ferencz: Electromagnetic wave propagation in general relativistic situation:: A general solution of the problem, Radio Science, Vol.47, RS1014, doi>10.1029/2011RS004905, 2012" in ch.4., during the solution we find a not too simple self consistent field situation. During the searching the solution we shall have equation-system in which the unknowns are the electromagnetic wave components and the space-time metric functions together. The boundary conditions are the "free space-time" components where no propagating electromagnetic field exists. (I am working to derive such kind of solutions and it seems to me, that it is possible to find these types of solutions.)
I.e. this possibility is not excluded, I hope.
If you got information that the universe can be modelled as 4d Klein bottle, would you begin to explore its deeper means on that basis?
Dear Esa,
Thank you for your answer. What would be the motivation for looking at the universe as a 4d Klein bottle?
My question relates asks if it makes sense to have a theory in which the metric depends on the scale under consideration. The reason I am asking this is because in the literature many use both de Sitter and Anti de Sitter and there are advantages to both. It seems in particular that at the particle scale AdS offers some advantages.
That is interesting. However, the reason I am interested in de Sitter and Anti de Sitter is because they are deformations of flat Minkowski space and their isometries are a Lie algebraic deformation from a non-rigid algebra (Poincare algebra) into a rigid one.
On 4d Klein bottle you can have as much positive and negative curvatures as needed for local gravity. Still the whole concept is globally flat. I suggest you can paste both de Sitter- and anti de Sitter -properties into the 4d Klein bottle but the universe is universally flat as observed until now. What important, infinities vanish nicely. AdS/CFT correspondence anomalies can be avoided. I see fermion duality as Möbius strip loops as see-saw time development of 3d surface constructing 4d Klein bottle...
- Badges
- Science method
- Similar topics
- Biological Science
- Ecology