On the dynamics of the universe in $D$ spatial dimensions

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 \citep{lima}. 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.

10 pages, 2 figures, Revista Mexicana de Astronomía y Astrofísica (in Press). arXiv admin note: text overlap with arXiv:astro-ph/0109215

Cited by in corpus (1)

• Some Relativistic and Gravitational Properties of the Wolfram Model