121404671
Spaces of positive and negative frequency solutions of field equations in curved space–times. I. The Klein–Gordon equation in stationary space–times
In stationary space–times Vn×R with compact space‐section manifold without boundary Vn, the Klein–Gordon equation is solved by the one‐parameter group of unitary operators generated by the energy operator i−1T−1 in the Sobolev spaces Hl(Vn) ×Hl−1(Vn). The canonical symplectic and complex structures of the associated dynamical system are calculated. The existence and the uniqueness of the Lichnerowicz kernel are established. The Hilbert spaces of positive and negative frequency‐part solutions defined by means of this kernel are constructed.
119721670
On quantization of free fields in stationary space-times
In Section 1 we analyse the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections; we give an existence and uniqueness theorem for the Lichnerowicz distribution kernelG1 together with its proper Fourier expansion, and we construct the Hilbert spaces of frequency-part solutions defined by means ofG1.In Section 2 an analysis, a theorem and a construction similar to the above are formulated for thefree real field spin 1, massm>0, in one kind of static space-times.In this letter, only results are given. For detailed proofs and further results, see reference [9], [10] and [11].
119252183
Gravitational waves during inflation from a 5D large-scale repulsive gravity model
Abstract We investigate, in the transverse traceless (TT) gauge, the generation of the relic background of gravitational waves, generated during the early inflationary stage, on the framework of a large-scale repulsive gravity model. We calculate the spectrum of the tensor metric fluctuations of an effective 4D Schwarzschild–de Sitter metric on cosmological scales. This metric is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution, in the context of a non-compact Kaluza–Klein theory of gravity. We found that the spectrum is nearly scale invariant under certain conditions. One interesting aspect of this model is that it is possible to derive the dynamical field equations for the tensor metric fluctuations, valid not just at cosmological scales, but also at astrophysical scales, from the same theoretical model. The astrophysical and cosmological scales are determined by the gravity–antigravity radius, which is a natural length scale of the model, that indicates when gravity becomes repulsive in nature.
121636708
Topological origin of the coupling constants hierarchy in Kaluza-Klein approach
We consider an Abelian BF-model in the frame of ten-dimensional Kaluza–Klein approach on the space T2×X×M, where X belongs to the class of four-dimension decorated plumbed cobordisms (dp-cobordisms) and M is an An-1-singularity resolution manifold homeomorphic to a compactified ALE space. These four-dimensional manifolds with boundaries possess nontrivial cohomology properties that lead to a specific generalization of the Dirac quantization conditions and enables us to express classical partition functions in terms of 4-form fluxes through the direct product of nontrivial 2-cycles associated with the manifolds X and M. The intersection matrices of these manifolds play the role of coupling constants for the fluxes. We build several examples of dp-cobordisms containing in their intersection matrices the hierarchy of dimensionless low-energy coupling constants of interactions which are available in the real universe. We also consider the phenomenon of "running coupling constants," in particular the cosmological constant evolution induced by the topology changes of internal space X.