Astronomisch Fysisch Onderzoek Nederland

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**Asfyon was founded in 1988 by a group of researchers and teachers in Holland and initiated by Dr Reinoud Jan Slagter**

*** alignment of quasar polarization axes and symmetry breaking in Einstein- scalar-gauge field theory

The easiest way to modify general relativity (GR) is to extend the spacetime to more then 4 dimensions. Modification seems to be necessary in order to overcome the serious problems which one encounters when one decreases the scale closer to the Planck scale. Specifically, the problems enclose the hierarchy problem, the cosmological constant problem, the fate of the black hole, the issue of dark energy and last but not least the handling of scales. There seems to be no limit on the smallness of fundamental units in one particular domain of physics, while in others there are very large space and time scales. A very attractive higher dimensional model is the so-called warped spacetime of Randall and Sundrum (RS), where there is one large extra dimension present. The result is that effective 4D Kaluza-Klein(KK) modes are obtained from the perturbative 5D graviton. These KK modes will be massive from the brane viewpoint. The modified Einstein equations on the brane and scalar gauge field equations will now contain contributions from the 5D Weyl tensor. The hierarchy problem is solved in these models, because the graviton's probability function is extremely high at the Planck-brane, but it drops exponentially as it moves closer towards the Tev-brane. Warped spacetimes can also be linked to conformal symmetry. Conformal invariance is a very approved property in string theory by the AdS/CFT correspondence, where a conformal field theory sits on the boundary of the Anti-DeSitter spacetime. Some decades ago 't Hooft proposed that the information about an extra dimension is visible as a curvature in a spacetime with one fewer dimension. So the fifth dimension can act as a spacetime fabric on the 4D boundary. The appearance of the five-dimensional curved spacetime is also natural from the black hole entropy. A five-dimensional black hole has entropy which is proportional to the five-dimensional “area.” But an “area” in five dimensions is a “volume” in four dimensions: this is appropriate as the entropy of a four-dimensional statistical system. Later it was realised that this principle can be reformulated as so-called AdS/CFT duality models. A famous example is the type IIB-string theory on the background of AdS_5 x S^5. It is equivalent to a (3+1)D super Yang-Mills model with U(N) symmetry living on the boundary. The AdS/CFT correspondence could even solve the black hole information paradox ( i.e., the unitarity paradox of time evolution). In the model of RS the gravitational degrees of freedom of the extra dimension appear on the brane as a dual field theory under AdS/CFT correspondence. So holography could be a prerequisite for the existence of such models. Since one believes that our universe is now expanding at an accelerating rate, a desirable situation would be that at early times the AdS/CFT correspondence holds and at later limes a dS/CFT correspondence. At any level, CI in GR remains a peculiar issue. There is the question if it is possible to incorporated other fields ( massless and massive) into conformal invariant GR. The resulting model should explain why in the high-energy situation mass scales are unimportant and could be of help to construct singularity-free spacetime by pushing them to infinity. Further, the notion of conformal null infinity and the definition of energy flux can be formulated. Conformal gauge-fixing procedures can also be linked by the upper limit of the amount of information that can be stored in a 5D spacetime, i.e., on a 4D hypersurface.The model can also have shortcomings, described as anomalies, i.e., will all the beta-functions of the conformal model vanish? It is hoped that at the quantum level anomalies can be removed and a kind of spontaneous symmetry breaking can be formulated at lower energies. By adding non-conformal mass to the Lagrangian (for example by a scalar gauge field with a potential term), does not affect the formal conformal invariance of the effective action after integrating over the dilaton field. We also have still the problem of the cosmological constant. The conformal symmetry will be possessed by the energy-momentum tensor, which will contain a dimensionful mass term in the potential of the Higgs field. A mass term breaks the tracelessness of the energy momentum tensor, unless a cosmological constant is also generated.

A related problem is the asymptotic flatness of isolated systems in GR, for example, the Kerr solution and possibly the controversial (rotating) cosmic string, especially when they radiate. There is a back-reaction of disturbances on the background metric: we have no flat metric in terms of which the falloff of the curvature can be specified. The problems concerning the notion of asymptotic flatness at null infinity, topological regularity, the gravitational energy emitted by compact objects and how to handle the limit as one goes to infinity, can more or less be, by postulating a strongly asymptotically predictable spacetime and the cosmic censor conjecture. In this approach one needs the redefinition of the spacetime, g= in order to be able to handle infinity. One introduces a dilaton field ω (or conformal factor), to be handled on an equal footing as the Higgs field. However, one should like to have , the flat Minkowski close to the Planck scale. The challenge is therefore to investigate the possibility that is emergent during the evolution of our universe. In general, one could say that a conformal structure for gravity is inevitable and is the missing symmetry for spacetimes. A warped U(1) scalar gauge field could also be used to explain the curious alignment of the polarization axes of quasars in large quasar groups on Mpc scales. This is possible a profound contribution to the energy-momentum tensor comes from the bulk spacetime and can be understand as "dark"-energy. The scalar field becomes super-massive by the contribution of the 5D Weyl tensor on the brane and stored azimuthal preferences of the spinning axes of the quasars just after the symmetry breaking. /