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arXiv · 0707.3387

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

R. F. L. Holanda·S. H. Pereira
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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 $p=ω_{D}ρ$. 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 $Λ$ 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.

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R. F. L. Holanda, S. H. Pereira. 2012-07-05. On the dynamics of the universe in $D$ spatial dimensions. https://arxiv.org/abs/0707.3387

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