Abstract
In this paper we present the equations of the evolution of the universe in D spatial dimensions, as a generalization of the work of Lima (2001). We discuss the Friedmann-Robertson-Walker cosmological equations in D spatial dimensions for a simple fluid with equation of state p=omega_{D} rho. It is possible to reduce the multidimensional equations to the equation of a point particle system subject to a linear force. This force can be expressed as an oscillator equation, anti-oscillator or a free particle equation, depending on the k parameter of the spatial curvature. An interesting result is the independence on the dimension D in a de Sitter evolution. We also stress the generality of this procedure with a cosmological Lambda term. A more interesting result is that the reduction of the dimensionality leads naturally to an accelerated expansion of the scale factor in the plane case.
