General solution of a cosmological model induced from higher dimensions using a kinematical constraint

TL;DR

This paper derives a general solution for a higher-dimensional cosmological model with a kinematical constraint, using Lie symmetries, applicable for any number of internal dimensions, and explores its cosmological implications.

Contribution

It provides a comprehensive, parametric solution for the model with arbitrary internal dimensions, extending previous work limited to three dimensions, and analyzes its cosmological behavior.

Findings

General solution derived for any number of internal dimensions

Parametric plots illustrating cosmological evolution for different n

Insights into the dynamical reduction process over cosmic time

Abstract

In a recent study Akarsu and Dereli (Gen. Relativ. Gravit. 45:1211, 2013) discussed the dynamical reduction of a higher dimensional cosmological model which is augmented by a kinematical constraint characterized by a single real parameter, correlating and controlling the expansion of both the external (physical) and internal spaces. In that paper explicit solutions were found only for the case of three dimensional internal space ($n=3$). Here we derive a general solution of the system using Lie group symmetry properties, in parametric form for arbitrary number $n=1,2,3,\dots$ of internal dimensions. We also investigate the dynamical reduction of the model as a function of cosmic time $t$ for various values of $n$ and generate parametric plots to discuss cosmologically relevant results.