Five Dimensional Cosmological Models in General Relativity

TL;DR

This paper explores five-dimensional Kaluza-Klein cosmological models within general relativity, analyzing how a variable gravitational constant and cosmological constant evolve over time in an expanding universe.

Contribution

It introduces a model with variable G and Λ in five dimensions, deriving their time dependence and linking them to the universe's expansion dynamics.

Findings

G decreases as t^{-(1-ω)} over time

Λ varies as t^{-2}, (dot R / R)^2, and (ddot R / R)

The universe exhibits expansion with specific variable G and Λ behaviors

Abstract

A Five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and $\Lambda$. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as $G \sim t^{-(1-\omega)}$ whereas the variation for the cosmological constant follows as $\Lambda \sim t^{-2}$, $\Lambda \sim (\dot R/R)^2$ and $\Lambda \sim \ddot R/R$ where $\omega$ is the equation of state parameter and $R$ is the scale factor.