Cosmology in an N-dimensional vector space

Previous results on a Geometrical Foundation for a Unified Field Theory are applied to the expanding universe. In the internal space the metric is chosen so that the curvature invariant depending on the internal variables is a constant (multiplied by a parameter depending on the space time variables), while the corresponding metric in the tangent space is that for a Friedmann universe of constant spatial curvature. The extra parameter is then determined from the consistency relations of the curvatures in the two spaces. Matter distributions can be taken into account by introducing a pressure p and density ρ connected by an equation of state, such as p ∼ ρ. The codetermined equations for fields arising from geometrical considerations and for the radial scale function have been solved in the particular caser of the field for a scalar meson, providing a possible source for the inflatory universe. (author). 12 refs