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Abstract : We propose in this research a new solution regarding the existence and the content of the initial spacetime singularity. In the context of topological field theory we consider that the initial singularity of space-time corresponds to a zero size singular gravitational instanton characterized by a Riemannian metric configuration (++++) in dimension D = 4. Connected with some unexpected topological data corresponding to the zero scale of space-time, the initial singularity is thus not considered in terms of divergences of physical fields but can be resolved in the frame of topological field theory. We get this result from the physical observation that the pre-spacetime is in a thermal equilibrium at the Planck scale. Therefore it should be subject to the KMS condition. We consequently consider that this KMS state might correspond to a unification between "physical state" (Planck scale) and "topological state" (zero scale). Then it is suggested that the "zero scale singularity" can be understood in terms of topological invariants, in particular the first Donaldson invariant. Therefore, we here introduce a new topological index, connected with 0 scale, of the form Z = Tr (-1)s, which we call "singularity invariant". Interestingly, this invariant corresponds also to the invariant topological current yield by the hyperfinite II* von Neumann algebra describing the zero scale of space-time. In such a context we conjecture that the problem of inertial interaction might be explained in terms of topological amplitude connected with the singular zero size gravitational instanton corresponding to the initial singularity of spacetime. Keywords : KMS State, topological field theory, singularity invariant, initial singularity, zero size instanton PACS : 0420D, 04.65.+e, 02.40.Xx, 04.60.-m, 05.45.-a
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Contributor : Bogdanoff Igor <>
Submitted on : Wednesday, July 24, 2002 - 1:49:24 AM
Last modification on : Friday, June 8, 2018 - 2:50:24 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 5:35:44 PM


  • HAL Id : tel-00001503, version 1


Igor Bogdanoff. ETAT TOPOLOGIQUE DE L'ESPACE TEMPS A ECHELLE 0. Physique mathématique [math-ph]. Université de Bourgogne, 2002. Français. ⟨tel-00001503v1⟩



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