One fundamental problem of modern physics is the search for a theory of everything able to explain the nature of space-time, what matter is and how matter interacts. There are various propositions, as Grand Unified Theory, Quantum Gravity, Supersymmetry, String and Superstring Theories, and M-Theory. However, none of them is able to consistently explain at the present and same time electromagnetism, relativity, gravitation, quantum physics and observed elementary particles. By developing a complete theory of the deformation of solid lattices using Euler’s coordinates, one finds that this one can be used for the description of the spatiotemporal evolution of the Universe instead of the general relativity. In this way, it is suggested that the Universe could be a massive elastic three-dimensional lattice described in the absolute space by using Euler’s coordinates, and that fundamental building blocks of Ordinary Matter could consist of topological singularities of this lattice, namely diverse dislocation loops, disclination loops and dispiration loops. One finds then, for an isotropic elastic lattice obeying Newton’s law, with specific assumptions on its elastic properties, that the behaviors of this lattice and of its topological defects display all known physics. Indeed, this theory contains intrinsically and allows one to deduce directly the various formalisms of electromagnetism, special relativity, general relativity, gravitation and quantum physics. It allows also one to give simple answers to some longstanding questions of modern cosmology, as the universe expansion, the big-bang and the dark energy. But it appears above all a completely new scalar charge, the curvature charge, which has no equivalence in the modern physical theories, which creates a very small deviation to the equivalence principle of Einstein between inertial mass and gravitational mass, and which allows one to give very simple explanations of the weak asymmetry observed between matter and anti-matter, the origin of the weak interaction force, the formation of galaxies, the disappearance of antimatter from the universe, the formation of gigantic black holes in the heart of the galaxies and the nature of the famous dark matter. Moreover, studying lattices with axial symmetries, one was able to identify a lattice structure whose topological defect loops coincide exactly with the complex zoology of elementary particles, and which allows one to explain quite simply the asymptotical behavior and the nature of the strong interaction force.
