Math

An ensemble of cosmological models based on generalized BF theory is constructed where the rôle of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed Vcobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions. PACS numbers: 0420G, 0240, 0460 Mathematics Department, CUCEI, University of Guadalajara, Guadalajara, Mexico. E-mail: efremov@udgserv.cencar.udg.mx Physics Department, CUCEI, University of Guadalajara, Guadalajara, Mexico. E-mail: mitskievich03@yahoo.com.mx

A cosmological model connecting the evolution of universe with a sequence of topology changes described by a collection of specific graph cobordisms, is constructed. It is shown that an adequate topological field theory (of BF-type) can be put into relation to each graph cobordism. The explicit expressions for transition amplitudes (partition functions) are written in these BF-models and it is shown that the basic topological invariants of the graph cobordisms (intersection matrices) play the r{\^o}le of coupling constants between the formal analogues of electric and magnetic fluxes quantized {\`a} la Dirac, but with the use of Poicar{\'e}--Lefschetz duality. For a specific graph cobordism, the diagonal elements and eigenvalues of the intersection matrix reproduce the hierarchy of dimensionless low-energy coupling constants of the fundamental interactions acting in the real universe.