Kaluza-Klein Type Robertson Walker Cosmological Model With Dynamical Cosmological Term $\Lambda$

TL;DR

This paper explores higher-dimensional Kaluza-Klein cosmological models with variable cosmological terms, deriving key cosmological distances and highlighting differences from four-dimensional models.

Contribution

It generalizes four-dimensional cosmological results to higher dimensions with variable mbda, analyzing different functional forms and their implications.

Findings

Equivalent matter and vacuum energy parameters in higher dimensions

Derived expressions for look back time, luminosity distance, angular diameter distance

Potential significant differences from four-dimensional models

Abstract

In this paper we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological models by considering three different forms of variable $\Lambda$: $\Lambda\sim(\frac{\dot{a}}{a})^2$,$\Lambda\sim(\frac{\ddot{a}} {a})$ and $\Lambda \sim \rho$. It is found that, the connecting free parameters of the models with cosmic matter and vacuum energy density parameters are equivalent, in the context of higher dimensional space time. The expression for the look back time, luminosity distance and angular diameter distance are also derived. This work has thus generalized to higher dimensions the well-known results in four dimensional space time. It is found that there may be significant difference in principle at least, from the analogous situation in four dimensional space time.