Noncompact Kaluza - Klein theory and inflationary cosmology : a complete formalism

A formalization of the recently introduced formalism for inflation is developed from a noncompact Kaluza-Klein theory. In particular, the case for a single scalar field inflationary model is studied. We obtain that the scalar potential, which assume different representations in different frames, has a geometrical origin. In the last years, many people has worked in extra dimensions [1]. As has been emphasized , Standard Model matter can propagate a large distance in extra dimensions without conflict with observations if Standard Model is confined to a (3+1)-dimensional subspace, or " 3-brane " , in the higher dimensions [2]. It should be possible if the four familiar dimensions where dependent of coordinate in the extra dimensions. In some works on non compact extra dimensions the authors studied trapping of matter fields to be effectively four dimensional (4D) [3] or studied finite-volume but topologically non compact extra dimensions [4]. A very important question in theoretical physics consists to provide a good geometrical description of matter using only one extra coordinate (say ψ). The explanation of this issue in the framework of the early universe, in particular for inflationary theory [5], should be of great importance in cosmology. In this letter, we are aimed to study this topic using the Kaluza-Klein formalism where the fifth coordinate is non compact. In this framework should be interesting to explain the origin of an effective four dimensional (4D) scalar potential V (ϕ) which could be originated from a 5D apparent vacuum. The idea that matter *