V.M. Simulik^1,, V.V. Rubish²

A brief history of dark matter (DM) and dark energy (DE) investigations is presented. The contemporary situation is discussed briefly as well. Our goal is to attract the attention to the essence of a geometric aspect of the problem. The role of the different spaces and corresponding phase transitions of the Universe is under special attention. Our own hypotheses that DM and DE are related to the space-time M(1,6) and to the Big Bang as a phase transition of the Universe are under consideration. In order to demonstrate the relationships between the M(1,6) and corresponding geometric Clifford algebras the Dirac-like equation with seven space-time derivatives and seven gamma matrices is considered. The link between this Dirac-like equation and the similar Maxwell equations is indicated. We pay some attention on the structure and nonhomogeneous character of the list of the higher dimensional Dirac equations. The necessity of step by step movement from ordinary to N-dimensional Dirac equation is demonstrated.

dark matter, dark energy, Clifford algebras, Dirac-like equation