New topological description of the Universe.

We extend the bimetric description of the Universe to a five-dimensional framework. Starting from Souriau’s work (1964) we use Robertson-Walker metrics, with an extra term corresponding to the additional Kaluza dimension. This first order model is limited to zero densities of electric charge and electromagnetic energy. Assuming that the massive particles, with positive or negative mass and energies have finite lifetimes, it restores the O(3) symmetry and makes the generalized gauge process to restart. As a consequence the speed of light tends to zero. We assume the Universe to be closed in all its dimensions. Then, following an idea introduced in 1994 we describe the Universe as the two folds cover of a projective space. The inversion of the arrow of time, mass and energy is a consequence of this geometrical hypothesis and fits the bimetric model. We choose to eliminate the “initial singularity ” replaced by a boundary space, which is found to be Euclidean