Abstract not found

This is a contribution on the controversy about junction conditions for classical signature change. The central issue in this debate is whether the extrinsic curvature on slices near the hypersurface of signature change has to be continuous (weak signature change) or to vanish (strong signature change). Led by a Lagrangian point of view, we write down eight candidate action functionals S1,...S8 as possible generalizations of general relativity and investigate to what extent each of these defines a sensible variational problem, and which junction condition is implied. Four of the actions involve an integration over the total manifold. A particular subtlety arises from the precise definition of the Einstein-Hilbert Lagrangian density |g | 1/2 R[g]. The other four actions are constructed as sums of integrals over singe-signature domains. The result is that both types of junction conditions occur in different models, i.e. are based on different first principles, none of which can be claimed to represent Work supported by the Austrian Academy of Sciences in the framework of the ”Austrian Programme for Advanced Research and Technology”. 0 the ”correct ” one, unless physical predictions are taken into account. From a point of view of naturality dictated by the variational formalism, weak signature change is slightly favoured over strong one, because it requires less à priori restrictions for the class of off-shell metrics. In addition, a proposal for the use of the Lagrangian framework in cosmology is made.

Using the concept of real tunneling configurations (classical signature change) and nucleation energy, we explore the consequences of an alternative minimization procedure for the Euclidean action in multiple-dimensional quantum cosmology. In both standard Hartle-Hawking type as well as Coleman type wormhole-based approaches, it is suggested that the action should be minimized among configurations of equal energy. In a simplified model, allowing for arbitrary products of spheres as Euclidean solutions, the favoured spacetime dimension is 4, the global topology of spacelike slices being S 1 ×S 2 (hence predicting a universe of Kantowski-Sachs type). There is, however, some freedom for a Kaluza-Klein scenario, in which case the observed spacelike slices are S 3. In this case, the internal space is a product of two-spheres, and the total space-time dimension is 6, 8, 10 or 12.

Recently, it has been shown that an infinite succession of classical signature changes (”signature oscillations”) can compactify and stabilize internal dimensions, and simultaneously leads, after a coarse graining type of average procedure, to an effective (”physical”) space-time geometry displaying the usual Lorentzian metric signature. Here, we consider a minimally coupled scalar field on such an oscillating background and study its effective dynamics. It turns out that the resulting field equation in four dimensions contains a coupling to some non-metric structure, the imprint of the ”microscopic” signature oscillations on the effective properties of matter. In a multidimensional FRW model, this structure is identical to a massive scalar field evolving in its homogeneous mode.

Distinguished solutions for discontinuous signature change with weak junction conditions

A real tunneling solution is an instanton for the Hartle-Hawking path integral with vanishing extrinsic curvature (vanishing “momentum”) at the boundary. Since the final momentum is fixed, its conjugate cannot be specified freely; consequently, such an instanton will contribute to the wave function at only one or a few isolated spatial geometries. I show that these geometries are the extrema of the Hartle-Hawking wave function in the semiclassical approximation, and provide some evidence that with a suitable choice of time parameter, these extrema are the maxima of the wave function at a fixed time.

Abstract not found