Mathematics – Logic
Scientific paper
Jun 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1241..487b&link_type=abstract
INVISIBLE UNIVERSE: Proceedings of the Conference. AIP Conference Proceedings, Volume 1241, pp. 487-496 (2010).
Mathematics
Logic
4
Dark Matter, Cosmology, Geodesy, Differential Equations, Dark Energy, Observational Cosmology, Geodesy And Gravity, Partial Differential Equations
Scientific paper
A new mathematical object more general than classical manifold is built, as a union of Hausdorff topological spaces all disjoint or all the same linked together with an internal structure and a diagonal topology. The construction of this mathematical object is made via quantified chain-react of double homeomorphisms over the graphs product of left and right mean functions. From the construction, it turns out that the mathematical object obtained is an expanding manifold where its basic elements are expanding and present new structures at every step of the chain react. A direct calculus of the distance between two distinct basic elements of the fractal manifold from one step to another leads directly to the Hubble's law which advocates to use the fractal manifold model in the description of the dynamic of our universe. A new metric of the space-time is then obtained. The geodesic of the light in this kind of space-time leads to the invisibility of the geometry of the universe, and to a natural distribution of matter into it. The space of our universe appears to be an infinite packed number of expanding basic elements in which the light is reflected only if it interacts with matter. It turns out that at the beginning of the expansion the different basic elements of the space start to expand simultaneously, from zero size, which creates the expansion and the distribution of matter we observe today, and this simultaneous expansion explains the homogeneity observed at large scale. The expansion of the basic elements of the space drives matter to be located on their boundaries, and matter appears then to be maintained everywhere in our universe by an invisible construction. A new interpretation of the dark energy is then obtained.
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