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

TL;DR

This paper generalizes the Friedmann-Robertson-Walker cosmological equations to D spatial dimensions, revealing how dimensionality affects universe evolution, including accelerated expansion and de Sitter solutions, with implications for higher-dimensional cosmology.

Contribution

It extends the standard cosmological equations to D dimensions and analyzes their solutions, highlighting effects of dimensionality on universe dynamics and acceleration.

Findings

De Sitter evolution is independent of dimension D.

Dimensional reduction can lead to accelerated expansion.

The equations can be reduced to a linear force system.

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.